Evaluate
\frac{5x^{2}+8x+2}{\left(x-7\right)\left(x+1\right)}
Expand
\frac{5x^{2}+8x+2}{\left(x-7\right)\left(x+1\right)}
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\frac{5x}{x-7}-\frac{-3x-2}{\left(x-7\right)\left(x+1\right)}
Factor x^{2}-6x-7.
\frac{5x\left(x+1\right)}{\left(x-7\right)\left(x+1\right)}-\frac{-3x-2}{\left(x-7\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-7 and \left(x-7\right)\left(x+1\right) is \left(x-7\right)\left(x+1\right). Multiply \frac{5x}{x-7} times \frac{x+1}{x+1}.
\frac{5x\left(x+1\right)-\left(-3x-2\right)}{\left(x-7\right)\left(x+1\right)}
Since \frac{5x\left(x+1\right)}{\left(x-7\right)\left(x+1\right)} and \frac{-3x-2}{\left(x-7\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x^{2}+5x+3x+2}{\left(x-7\right)\left(x+1\right)}
Do the multiplications in 5x\left(x+1\right)-\left(-3x-2\right).
\frac{5x^{2}+8x+2}{\left(x-7\right)\left(x+1\right)}
Combine like terms in 5x^{2}+5x+3x+2.
\frac{5x^{2}+8x+2}{x^{2}-6x-7}
Expand \left(x-7\right)\left(x+1\right).
\frac{5x}{x-7}-\frac{-3x-2}{\left(x-7\right)\left(x+1\right)}
Factor x^{2}-6x-7.
\frac{5x\left(x+1\right)}{\left(x-7\right)\left(x+1\right)}-\frac{-3x-2}{\left(x-7\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-7 and \left(x-7\right)\left(x+1\right) is \left(x-7\right)\left(x+1\right). Multiply \frac{5x}{x-7} times \frac{x+1}{x+1}.
\frac{5x\left(x+1\right)-\left(-3x-2\right)}{\left(x-7\right)\left(x+1\right)}
Since \frac{5x\left(x+1\right)}{\left(x-7\right)\left(x+1\right)} and \frac{-3x-2}{\left(x-7\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x^{2}+5x+3x+2}{\left(x-7\right)\left(x+1\right)}
Do the multiplications in 5x\left(x+1\right)-\left(-3x-2\right).
\frac{5x^{2}+8x+2}{\left(x-7\right)\left(x+1\right)}
Combine like terms in 5x^{2}+5x+3x+2.
\frac{5x^{2}+8x+2}{x^{2}-6x-7}
Expand \left(x-7\right)\left(x+1\right).
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Simultaneous equation
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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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