Solve 5x+10/x-1-2x-3/4=

$$\frac { 5 x + 10 } { x - 1 } - \frac { 2 x - 3 } { 4 } =$$

Evaluate

$$\frac{37+25x-2x^{2}}{4\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 4 is 4\left(x-1\right). Multiply \frac{5x+10}{x-1} times \frac{4}{4}. Multiply \frac{2x-3}{4} times \frac{x-1}{x-1}.

$$\frac{4\left(5x+10\right)}{4\left(x-1\right)}-\frac{\left(2x-3\right)\left(x-1\right)}{4\left(x-1\right)}$$

Since \frac{4\left(5x+10\right)}{4\left(x-1\right)} and \frac{\left(2x-3\right)\left(x-1\right)}{4\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(5x+10\right)-\left(2x-3\right)\left(x-1\right)}{4\left(x-1\right)}$$

Do the multiplications in 4\left(5x+10\right)-\left(2x-3\right)\left(x-1\right).

$$\frac{20x+40-2x^{2}+2x+3x-3}{4\left(x-1\right)}$$

Combine like terms in 20x+40-2x^{2}+2x+3x-3.

$$\frac{25x+37-2x^{2}}{4\left(x-1\right)}$$

Factor the expressions that are not already factored in \frac{25x+37-2x^{2}}{4\left(x-1\right)}.

$$\frac{-2\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{4\left(x-1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2\left(x-1\right)}$$

Expand 2\left(x-1\right).

$$\frac{-\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2x-2}$$

To find the opposite of -\frac{1}{4}\sqrt{921}+\frac{25}{4}, find the opposite of each term.

$$\frac{-\left(x-\left(-\frac{1}{4}\sqrt{921}\right)-\frac{25}{4}\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2x-2}$$

The opposite of -\frac{1}{4}\sqrt{921} is \frac{1}{4}\sqrt{921}.

$$\frac{-\left(x+\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2x-2}$$

To find the opposite of \frac{1}{4}\sqrt{921}+\frac{25}{4}, find the opposite of each term.

$$\frac{-\left(x+\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)\left(x-\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)}{2x-2}$$

Use the distributive property to multiply -1 by x+\frac{1}{4}\sqrt{921}-\frac{25}{4}.

$$\frac{\left(-x-\frac{1}{4}\sqrt{921}-\left(-\frac{25}{4}\right)\right)\left(x-\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)}{2x-2}$$

Multiply -1 and -\frac{25}{4} to get \frac{25}{4}.

$$\frac{\left(-x-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\left(x-\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)}{2x-2}$$

Apply the distributive property by multiplying each term of -x-\frac{1}{4}\sqrt{921}+\frac{25}{4} by each term of x-\frac{1}{4}\sqrt{921}-\frac{25}{4}.

$$\frac{-x^{2}-x\left(-\frac{1}{4}\right)\sqrt{921}-x\left(-\frac{25}{4}\right)-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\sqrt{921}\left(-\frac{1}{4}\right)\sqrt{921}-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply \sqrt{921} and \sqrt{921} to get 921.

$$\frac{-x^{2}-x\left(-\frac{1}{4}\right)\sqrt{921}-x\left(-\frac{25}{4}\right)-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -1 and -\frac{1}{4} to get \frac{1}{4}.

$$\frac{-x^{2}+\frac{1}{4}x\sqrt{921}-x\left(-\frac{25}{4}\right)-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -1 and -\frac{25}{4} to get \frac{25}{4}.

$$\frac{-x^{2}+\frac{1}{4}x\sqrt{921}+\frac{25}{4}x-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Combine \frac{1}{4}x\sqrt{921} and -\frac{1}{4}\sqrt{921}x to get 0.

$$\frac{-x^{2}+\frac{25}{4}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Express -\frac{1}{4}\times 921 as a single fraction.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{-921}{4}\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Fraction \frac{-921}{4} can be rewritten as -\frac{921}{4} by extracting the negative sign.

$$\frac{-x^{2}+\frac{25}{4}x-\frac{921}{4}\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -\frac{921}{4} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{-921\left(-1\right)}{4\times 4}-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Do the multiplications in the fraction \frac{-921\left(-1\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{921}{16}-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -\frac{1}{4} times -\frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{921}{16}+\frac{-\left(-25\right)}{4\times 4}\sqrt{921}+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Do the multiplications in the fraction \frac{-\left(-25\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Combine \frac{25}{4}x and \frac{25}{4}x to get \frac{25}{2}x.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply \frac{25}{4} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{25\left(-1\right)}{4\times 4}\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Do the multiplications in the fraction \frac{25\left(-1\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{-25}{16}\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Fraction \frac{-25}{16} can be rewritten as -\frac{25}{16} by extracting the negative sign.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}-\frac{25}{16}\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Combine \frac{25}{16}\sqrt{921} and -\frac{25}{16}\sqrt{921} to get 0.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply \frac{25}{4} times -\frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25\left(-25\right)}{4\times 4}}{2x-2}$$

Do the multiplications in the fraction \frac{25\left(-25\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{-625}{16}}{2x-2}$$

Fraction \frac{-625}{16} can be rewritten as -\frac{625}{16} by extracting the negative sign.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}-\frac{625}{16}}{2x-2}$$

Since \frac{921}{16} and \frac{625}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921-625}{16}}{2x-2}$$

Subtract 625 from 921 to get 296.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{296}{16}}{2x-2}$$

Reduce the fraction \frac{296}{16} to lowest terms by extracting and canceling out 8.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{37}{2}}{2x-2}$$

Factor the expressions that are not already factored.

$$\frac{-\frac{1}{2}\times 2\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2\left(x-1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\frac{1}{2}\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{x-1}$$

Expand the expression.

$$\frac{-\frac{1}{2}x^{2}+\frac{25}{4}x+\frac{37}{4}}{x-1}$$

Expand

$$-\frac{2x^{2}-25x-37}{4\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 4 is 4\left(x-1\right). Multiply \frac{5x+10}{x-1} times \frac{4}{4}. Multiply \frac{2x-3}{4} times \frac{x-1}{x-1}.

$$\frac{4\left(5x+10\right)}{4\left(x-1\right)}-\frac{\left(2x-3\right)\left(x-1\right)}{4\left(x-1\right)}$$

Since \frac{4\left(5x+10\right)}{4\left(x-1\right)} and \frac{\left(2x-3\right)\left(x-1\right)}{4\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(5x+10\right)-\left(2x-3\right)\left(x-1\right)}{4\left(x-1\right)}$$

Do the multiplications in 4\left(5x+10\right)-\left(2x-3\right)\left(x-1\right).

$$\frac{20x+40-2x^{2}+2x+3x-3}{4\left(x-1\right)}$$

Combine like terms in 20x+40-2x^{2}+2x+3x-3.

$$\frac{25x+37-2x^{2}}{4\left(x-1\right)}$$

Factor the expressions that are not already factored in \frac{25x+37-2x^{2}}{4\left(x-1\right)}.

$$\frac{-2\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{4\left(x-1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2\left(x-1\right)}$$

Expand 2\left(x-1\right).

$$\frac{-\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2x-2}$$

To find the opposite of -\frac{1}{4}\sqrt{921}+\frac{25}{4}, find the opposite of each term.

$$\frac{-\left(x-\left(-\frac{1}{4}\sqrt{921}\right)-\frac{25}{4}\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2x-2}$$

The opposite of -\frac{1}{4}\sqrt{921} is \frac{1}{4}\sqrt{921}.

$$\frac{-\left(x+\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2x-2}$$

To find the opposite of \frac{1}{4}\sqrt{921}+\frac{25}{4}, find the opposite of each term.

$$\frac{-\left(x+\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)\left(x-\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)}{2x-2}$$

Use the distributive property to multiply -1 by x+\frac{1}{4}\sqrt{921}-\frac{25}{4}.

$$\frac{\left(-x-\frac{1}{4}\sqrt{921}-\left(-\frac{25}{4}\right)\right)\left(x-\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)}{2x-2}$$

Multiply -1 and -\frac{25}{4} to get \frac{25}{4}.

$$\frac{\left(-x-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\left(x-\frac{1}{4}\sqrt{921}-\frac{25}{4}\right)}{2x-2}$$

Apply the distributive property by multiplying each term of -x-\frac{1}{4}\sqrt{921}+\frac{25}{4} by each term of x-\frac{1}{4}\sqrt{921}-\frac{25}{4}.

$$\frac{-x^{2}-x\left(-\frac{1}{4}\right)\sqrt{921}-x\left(-\frac{25}{4}\right)-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\sqrt{921}\left(-\frac{1}{4}\right)\sqrt{921}-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply \sqrt{921} and \sqrt{921} to get 921.

$$\frac{-x^{2}-x\left(-\frac{1}{4}\right)\sqrt{921}-x\left(-\frac{25}{4}\right)-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -1 and -\frac{1}{4} to get \frac{1}{4}.

$$\frac{-x^{2}+\frac{1}{4}x\sqrt{921}-x\left(-\frac{25}{4}\right)-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -1 and -\frac{25}{4} to get \frac{25}{4}.

$$\frac{-x^{2}+\frac{1}{4}x\sqrt{921}+\frac{25}{4}x-\frac{1}{4}\sqrt{921}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Combine \frac{1}{4}x\sqrt{921} and -\frac{1}{4}\sqrt{921}x to get 0.

$$\frac{-x^{2}+\frac{25}{4}x-\frac{1}{4}\times 921\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Express -\frac{1}{4}\times 921 as a single fraction.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{-921}{4}\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Fraction \frac{-921}{4} can be rewritten as -\frac{921}{4} by extracting the negative sign.

$$\frac{-x^{2}+\frac{25}{4}x-\frac{921}{4}\left(-\frac{1}{4}\right)-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -\frac{921}{4} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{-921\left(-1\right)}{4\times 4}-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Do the multiplications in the fraction \frac{-921\left(-1\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{921}{16}-\frac{1}{4}\sqrt{921}\left(-\frac{25}{4}\right)+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply -\frac{1}{4} times -\frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{921}{16}+\frac{-\left(-25\right)}{4\times 4}\sqrt{921}+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Do the multiplications in the fraction \frac{-\left(-25\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{4}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{25}{4}x+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Combine \frac{25}{4}x and \frac{25}{4}x to get \frac{25}{2}x.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{25}{4}\left(-\frac{1}{4}\right)\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply \frac{25}{4} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{25\left(-1\right)}{4\times 4}\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Do the multiplications in the fraction \frac{25\left(-1\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}+\frac{-25}{16}\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Fraction \frac{-25}{16} can be rewritten as -\frac{25}{16} by extracting the negative sign.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{16}\sqrt{921}-\frac{25}{16}\sqrt{921}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Combine \frac{25}{16}\sqrt{921} and -\frac{25}{16}\sqrt{921} to get 0.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25}{4}\left(-\frac{25}{4}\right)}{2x-2}$$

Multiply \frac{25}{4} times -\frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{25\left(-25\right)}{4\times 4}}{2x-2}$$

Do the multiplications in the fraction \frac{25\left(-25\right)}{4\times 4}.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}+\frac{-625}{16}}{2x-2}$$

Fraction \frac{-625}{16} can be rewritten as -\frac{625}{16} by extracting the negative sign.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921}{16}-\frac{625}{16}}{2x-2}$$

Since \frac{921}{16} and \frac{625}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{921-625}{16}}{2x-2}$$

Subtract 625 from 921 to get 296.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{296}{16}}{2x-2}$$

Reduce the fraction \frac{296}{16} to lowest terms by extracting and canceling out 8.

$$\frac{-x^{2}+\frac{25}{2}x+\frac{37}{2}}{2x-2}$$

Factor the expressions that are not already factored.

$$\frac{-\frac{1}{2}\times 2\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{2\left(x-1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\frac{1}{2}\left(x-\left(-\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{921}+\frac{25}{4}\right)\right)}{x-1}$$

Expand the expression.

$$\frac{-\frac{1}{2}x^{2}+\frac{25}{4}x+\frac{37}{4}}{x-1}$$