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\frac{c-7}{c+7}
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\frac{c-7}{c+7}
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\frac{c+7}{c-7}+\frac{28c}{\left(c-7\right)\left(-c-7\right)}
Factor 49-c^{2}.
\frac{\left(c+7\right)\left(-c-7\right)}{\left(c-7\right)\left(-c-7\right)}+\frac{28c}{\left(c-7\right)\left(-c-7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c-7 and \left(c-7\right)\left(-c-7\right) is \left(c-7\right)\left(-c-7\right). Multiply \frac{c+7}{c-7} times \frac{-c-7}{-c-7}.
\frac{\left(c+7\right)\left(-c-7\right)+28c}{\left(c-7\right)\left(-c-7\right)}
Since \frac{\left(c+7\right)\left(-c-7\right)}{\left(c-7\right)\left(-c-7\right)} and \frac{28c}{\left(c-7\right)\left(-c-7\right)} have the same denominator, add them by adding their numerators.
\frac{-c^{2}-7c-7c-49+28c}{\left(c-7\right)\left(-c-7\right)}
Do the multiplications in \left(c+7\right)\left(-c-7\right)+28c.
\frac{-c^{2}+14c-49}{\left(c-7\right)\left(-c-7\right)}
Combine like terms in -c^{2}-7c-7c-49+28c.
\frac{\left(c-7\right)\left(-c+7\right)}{\left(c-7\right)\left(-c-7\right)}
Factor the expressions that are not already factored in \frac{-c^{2}+14c-49}{\left(c-7\right)\left(-c-7\right)}.
\frac{-\left(c-7\right)\left(c-7\right)}{\left(c-7\right)\left(-c-7\right)}
Extract the negative sign in 7-c.
\frac{-\left(c-7\right)}{-c-7}
Cancel out c-7 in both numerator and denominator.
\frac{-c+7}{-c-7}
To find the opposite of c-7, find the opposite of each term.
\frac{c+7}{c-7}+\frac{28c}{\left(c-7\right)\left(-c-7\right)}
Factor 49-c^{2}.
\frac{\left(c+7\right)\left(-c-7\right)}{\left(c-7\right)\left(-c-7\right)}+\frac{28c}{\left(c-7\right)\left(-c-7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c-7 and \left(c-7\right)\left(-c-7\right) is \left(c-7\right)\left(-c-7\right). Multiply \frac{c+7}{c-7} times \frac{-c-7}{-c-7}.
\frac{\left(c+7\right)\left(-c-7\right)+28c}{\left(c-7\right)\left(-c-7\right)}
Since \frac{\left(c+7\right)\left(-c-7\right)}{\left(c-7\right)\left(-c-7\right)} and \frac{28c}{\left(c-7\right)\left(-c-7\right)} have the same denominator, add them by adding their numerators.
\frac{-c^{2}-7c-7c-49+28c}{\left(c-7\right)\left(-c-7\right)}
Do the multiplications in \left(c+7\right)\left(-c-7\right)+28c.
\frac{-c^{2}+14c-49}{\left(c-7\right)\left(-c-7\right)}
Combine like terms in -c^{2}-7c-7c-49+28c.
\frac{\left(c-7\right)\left(-c+7\right)}{\left(c-7\right)\left(-c-7\right)}
Factor the expressions that are not already factored in \frac{-c^{2}+14c-49}{\left(c-7\right)\left(-c-7\right)}.
\frac{-\left(c-7\right)\left(c-7\right)}{\left(c-7\right)\left(-c-7\right)}
Extract the negative sign in 7-c.
\frac{-\left(c-7\right)}{-c-7}
Cancel out c-7 in both numerator and denominator.
\frac{-c+7}{-c-7}
To find the opposite of c-7, find the opposite of each term.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}