Evaluate
\frac{7}{\left(x+3\right)\left(x+7\right)}
Expand
\frac{7}{\left(x+3\right)\left(x+7\right)}
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\frac{x-3}{x^{2}-2x+7x-14}\times \frac{7x-14}{\left(x+3\right)\left(x-3\right)}
Apply the distributive property by multiplying each term of x+7 by each term of x-2.
\frac{x-3}{x^{2}+5x-14}\times \frac{7x-14}{\left(x+3\right)\left(x-3\right)}
Combine -2x and 7x to get 5x.
\frac{x-3}{x^{2}+5x-14}\times \frac{7x-14}{x^{2}-3^{2}}
Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{x-3}{x^{2}+5x-14}\times \frac{7x-14}{x^{2}-9}
Calculate 3 to the power of 2 and get 9.
\frac{\left(x-3\right)\left(7x-14\right)}{\left(x^{2}+5x-14\right)\left(x^{2}-9\right)}
Multiply \frac{x-3}{x^{2}+5x-14} times \frac{7x-14}{x^{2}-9} by multiplying numerator times numerator and denominator times denominator.
\frac{7\left(x-3\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x+3\right)\left(x+7\right)}
Factor the expressions that are not already factored.
\frac{7}{\left(x+3\right)\left(x+7\right)}
Cancel out \left(x-3\right)\left(x-2\right) in both numerator and denominator.
\frac{7}{x^{2}+10x+21}
Expand the expression.
\frac{x-3}{x^{2}-2x+7x-14}\times \frac{7x-14}{\left(x+3\right)\left(x-3\right)}
Apply the distributive property by multiplying each term of x+7 by each term of x-2.
\frac{x-3}{x^{2}+5x-14}\times \frac{7x-14}{\left(x+3\right)\left(x-3\right)}
Combine -2x and 7x to get 5x.
\frac{x-3}{x^{2}+5x-14}\times \frac{7x-14}{x^{2}-3^{2}}
Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{x-3}{x^{2}+5x-14}\times \frac{7x-14}{x^{2}-9}
Calculate 3 to the power of 2 and get 9.
\frac{\left(x-3\right)\left(7x-14\right)}{\left(x^{2}+5x-14\right)\left(x^{2}-9\right)}
Multiply \frac{x-3}{x^{2}+5x-14} times \frac{7x-14}{x^{2}-9} by multiplying numerator times numerator and denominator times denominator.
\frac{7\left(x-3\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x+3\right)\left(x+7\right)}
Factor the expressions that are not already factored.
\frac{7}{\left(x+3\right)\left(x+7\right)}
Cancel out \left(x-3\right)\left(x-2\right) in both numerator and denominator.
\frac{7}{x^{2}+10x+21}
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}