Solve 3-4/a-1/5-frac{3{1-a}}

$$\frac { 3 - \frac { 4 } { a - 1 } } { 5 - \frac { 3 } { 1 - a } }$$

Evaluate

$$-\frac{3a-7}{2-5a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a-1}{a-1}.

$$\frac{\frac{3\left(a-1\right)}{a-1}-\frac{4}{a-1}}{5-\frac{3}{1-a}}$$

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

$$\frac{\frac{3\left(a-1\right)-4}{a-1}}{5-\frac{3}{1-a}}$$

Do the multiplications in 3\left(a-1\right)-4.

$$\frac{\frac{3a-3-4}{a-1}}{5-\frac{3}{1-a}}$$

Combine like terms in 3a-3-4.

$$\frac{\frac{3a-7}{a-1}}{5-\frac{3}{1-a}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{1-a}{1-a}.

$$\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)}{1-a}-\frac{3}{1-a}}$$

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

$$\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)-3}{1-a}}$$

Do the multiplications in 5\left(1-a\right)-3.

$$\frac{\frac{3a-7}{a-1}}{\frac{5-5a-3}{1-a}}$$

Combine like terms in 5-5a-3.

$$\frac{\frac{3a-7}{a-1}}{\frac{2-5a}{1-a}}$$

Divide \frac{3a-7}{a-1} by \frac{2-5a}{1-a} by multiplying \frac{3a-7}{a-1} by the reciprocal of \frac{2-5a}{1-a}.

$$\frac{\left(3a-7\right)\left(1-a\right)}{\left(a-1\right)\left(2-5a\right)}$$

Extract the negative sign in 1-a.

$$\frac{-\left(a-1\right)\left(3a-7\right)}{\left(a-1\right)\left(-5a+2\right)}$$

Cancel out a-1 in both numerator and denominator.

$$\frac{-\left(3a-7\right)}{-5a+2}$$

To find the opposite of 3a-7, find the opposite of each term.

$$\frac{-3a-\left(-7\right)}{-5a+2}$$

The opposite of -7 is 7.

$$\frac{-3a+7}{-5a+2}$$

Expand

$$-\frac{3a-7}{2-5a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a-1}{a-1}.

$$\frac{\frac{3\left(a-1\right)}{a-1}-\frac{4}{a-1}}{5-\frac{3}{1-a}}$$

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

$$\frac{\frac{3\left(a-1\right)-4}{a-1}}{5-\frac{3}{1-a}}$$

Do the multiplications in 3\left(a-1\right)-4.

$$\frac{\frac{3a-3-4}{a-1}}{5-\frac{3}{1-a}}$$

Combine like terms in 3a-3-4.

$$\frac{\frac{3a-7}{a-1}}{5-\frac{3}{1-a}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{1-a}{1-a}.

$$\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)}{1-a}-\frac{3}{1-a}}$$

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

$$\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)-3}{1-a}}$$

Do the multiplications in 5\left(1-a\right)-3.

$$\frac{\frac{3a-7}{a-1}}{\frac{5-5a-3}{1-a}}$$

Combine like terms in 5-5a-3.

$$\frac{\frac{3a-7}{a-1}}{\frac{2-5a}{1-a}}$$

Divide \frac{3a-7}{a-1} by \frac{2-5a}{1-a} by multiplying \frac{3a-7}{a-1} by the reciprocal of \frac{2-5a}{1-a}.

$$\frac{\left(3a-7\right)\left(1-a\right)}{\left(a-1\right)\left(2-5a\right)}$$

Extract the negative sign in 1-a.

$$\frac{-\left(a-1\right)\left(3a-7\right)}{\left(a-1\right)\left(-5a+2\right)}$$

Cancel out a-1 in both numerator and denominator.

$$\frac{-\left(3a-7\right)}{-5a+2}$$

To find the opposite of 3a-7, find the opposite of each term.

$$\frac{-3a-\left(-7\right)}{-5a+2}$$

The opposite of -7 is 7.

$$\frac{-3a+7}{-5a+2}$$