Evaluate
\frac{\left(c-7\right)\left(c+3\right)}{\left(c+1\right)\left(c+6\right)}
Expand
\frac{c^{2}-4c-21}{\left(c+1\right)\left(c+6\right)}
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\frac{\left(c+3\right)\left(c-7\right)}{\left(c+1\right)\left(c+6\right)}
Divide \frac{c+3}{c+1} by \frac{c+6}{c-7} by multiplying \frac{c+3}{c+1} by the reciprocal of \frac{c+6}{c-7}.
\frac{c^{2}-7c+3c-21}{\left(c+1\right)\left(c+6\right)}
Apply the distributive property by multiplying each term of c+3 by each term of c-7.
\frac{c^{2}-4c-21}{\left(c+1\right)\left(c+6\right)}
Combine -7c and 3c to get -4c.
\frac{c^{2}-4c-21}{c^{2}+6c+c+6}
Apply the distributive property by multiplying each term of c+1 by each term of c+6.
\frac{c^{2}-4c-21}{c^{2}+7c+6}
Combine 6c and c to get 7c.
\frac{\left(c+3\right)\left(c-7\right)}{\left(c+1\right)\left(c+6\right)}
Divide \frac{c+3}{c+1} by \frac{c+6}{c-7} by multiplying \frac{c+3}{c+1} by the reciprocal of \frac{c+6}{c-7}.
\frac{c^{2}-7c+3c-21}{\left(c+1\right)\left(c+6\right)}
Apply the distributive property by multiplying each term of c+3 by each term of c-7.
\frac{c^{2}-4c-21}{\left(c+1\right)\left(c+6\right)}
Combine -7c and 3c to get -4c.
\frac{c^{2}-4c-21}{c^{2}+6c+c+6}
Apply the distributive property by multiplying each term of c+1 by each term of c+6.
\frac{c^{2}-4c-21}{c^{2}+7c+6}
Combine 6c and c to get 7c.
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}