Evaluate
\frac{2x-5}{\left(x+2\right)\left(x+7\right)}
Expand
\frac{2x-5}{\left(x+2\right)\left(x+7\right)}
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\frac{8x-20}{\left(x-5\right)\left(x+7\right)}\times \frac{\left(x-5\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}
Use the distributive property to multiply 4 by 2x-5.
\frac{8x-20}{x^{2}+7x-5x-35}\times \frac{\left(x-5\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}
Apply the distributive property by multiplying each term of x-5 by each term of x+7.
\frac{8x-20}{x^{2}+2x-35}\times \frac{\left(x-5\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}
Combine 7x and -5x to get 2x.
\frac{8x-20}{x^{2}+2x-35}\times \frac{x-5}{4\left(x+2\right)}
Cancel out x-2 in both numerator and denominator.
\frac{\left(8x-20\right)\left(x-5\right)}{\left(x^{2}+2x-35\right)\times 4\left(x+2\right)}
Multiply \frac{8x-20}{x^{2}+2x-35} times \frac{x-5}{4\left(x+2\right)} by multiplying numerator times numerator and denominator times denominator.
\frac{4\left(x-5\right)\left(2x-5\right)}{4\left(x-5\right)\left(x+2\right)\left(x+7\right)}
Factor the expressions that are not already factored.
\frac{2x-5}{\left(x+2\right)\left(x+7\right)}
Cancel out 4\left(x-5\right) in both numerator and denominator.
\frac{2x-5}{x^{2}+9x+14}
Expand the expression.
\frac{8x-20}{\left(x-5\right)\left(x+7\right)}\times \frac{\left(x-5\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}
Use the distributive property to multiply 4 by 2x-5.
\frac{8x-20}{x^{2}+7x-5x-35}\times \frac{\left(x-5\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}
Apply the distributive property by multiplying each term of x-5 by each term of x+7.
\frac{8x-20}{x^{2}+2x-35}\times \frac{\left(x-5\right)\left(x-2\right)}{4\left(x-2\right)\left(x+2\right)}
Combine 7x and -5x to get 2x.
\frac{8x-20}{x^{2}+2x-35}\times \frac{x-5}{4\left(x+2\right)}
Cancel out x-2 in both numerator and denominator.
\frac{\left(8x-20\right)\left(x-5\right)}{\left(x^{2}+2x-35\right)\times 4\left(x+2\right)}
Multiply \frac{8x-20}{x^{2}+2x-35} times \frac{x-5}{4\left(x+2\right)} by multiplying numerator times numerator and denominator times denominator.
\frac{4\left(x-5\right)\left(2x-5\right)}{4\left(x-5\right)\left(x+2\right)\left(x+7\right)}
Factor the expressions that are not already factored.
\frac{2x-5}{\left(x+2\right)\left(x+7\right)}
Cancel out 4\left(x-5\right) in both numerator and denominator.
\frac{2x-5}{x^{2}+9x+14}
Expand the expression.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}