Evaluate
\frac{28x^{2}-85x-5}{\left(x-8\right)\left(4x-5\right)}
Expand
\frac{28x^{2}-85x-5}{\left(x-8\right)\left(4x-5\right)}
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\frac{\left(5x+1\right)\left(4x-5\right)}{\left(x-8\right)\left(4x-5\right)}+\frac{8x\left(x-8\right)}{\left(x-8\right)\left(4x-5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-8 and 4x-5 is \left(x-8\right)\left(4x-5\right). Multiply \frac{5x+1}{x-8} times \frac{4x-5}{4x-5}. Multiply \frac{8x}{4x-5} times \frac{x-8}{x-8}.
\frac{\left(5x+1\right)\left(4x-5\right)+8x\left(x-8\right)}{\left(x-8\right)\left(4x-5\right)}
Since \frac{\left(5x+1\right)\left(4x-5\right)}{\left(x-8\right)\left(4x-5\right)} and \frac{8x\left(x-8\right)}{\left(x-8\right)\left(4x-5\right)} have the same denominator, add them by adding their numerators.
\frac{20x^{2}-25x+4x-5+8x^{2}-64x}{\left(x-8\right)\left(4x-5\right)}
Do the multiplications in \left(5x+1\right)\left(4x-5\right)+8x\left(x-8\right).
\frac{28x^{2}-85x-5}{\left(x-8\right)\left(4x-5\right)}
Combine like terms in 20x^{2}-25x+4x-5+8x^{2}-64x.
\frac{28x^{2}-85x-5}{4x^{2}-37x+40}
Expand \left(x-8\right)\left(4x-5\right).
\frac{\left(5x+1\right)\left(4x-5\right)}{\left(x-8\right)\left(4x-5\right)}+\frac{8x\left(x-8\right)}{\left(x-8\right)\left(4x-5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-8 and 4x-5 is \left(x-8\right)\left(4x-5\right). Multiply \frac{5x+1}{x-8} times \frac{4x-5}{4x-5}. Multiply \frac{8x}{4x-5} times \frac{x-8}{x-8}.
\frac{\left(5x+1\right)\left(4x-5\right)+8x\left(x-8\right)}{\left(x-8\right)\left(4x-5\right)}
Since \frac{\left(5x+1\right)\left(4x-5\right)}{\left(x-8\right)\left(4x-5\right)} and \frac{8x\left(x-8\right)}{\left(x-8\right)\left(4x-5\right)} have the same denominator, add them by adding their numerators.
\frac{20x^{2}-25x+4x-5+8x^{2}-64x}{\left(x-8\right)\left(4x-5\right)}
Do the multiplications in \left(5x+1\right)\left(4x-5\right)+8x\left(x-8\right).
\frac{28x^{2}-85x-5}{\left(x-8\right)\left(4x-5\right)}
Combine like terms in 20x^{2}-25x+4x-5+8x^{2}-64x.
\frac{28x^{2}-85x-5}{4x^{2}-37x+40}
Expand \left(x-8\right)\left(4x-5\right).
Examples
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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