Evaluate
\frac{4r+53}{\left(r-9\right)\left(r-7\right)}
Expand
\frac{4r+53}{\left(r-9\right)\left(r-7\right)}
Share
Copied to clipboard
\frac{10r-1}{\left(r-9\right)\left(r-7\right)}-\frac{6}{r-7}
Factor r^{2}-16r+63.
\frac{10r-1}{\left(r-9\right)\left(r-7\right)}-\frac{6\left(r-9\right)}{\left(r-9\right)\left(r-7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(r-9\right)\left(r-7\right) and r-7 is \left(r-9\right)\left(r-7\right). Multiply \frac{6}{r-7} times \frac{r-9}{r-9}.
\frac{10r-1-6\left(r-9\right)}{\left(r-9\right)\left(r-7\right)}
Since \frac{10r-1}{\left(r-9\right)\left(r-7\right)} and \frac{6\left(r-9\right)}{\left(r-9\right)\left(r-7\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{10r-1-6r+54}{\left(r-9\right)\left(r-7\right)}
Do the multiplications in 10r-1-6\left(r-9\right).
\frac{4r+53}{\left(r-9\right)\left(r-7\right)}
Combine like terms in 10r-1-6r+54.
\frac{4r+53}{r^{2}-16r+63}
Expand \left(r-9\right)\left(r-7\right).
\frac{10r-1}{\left(r-9\right)\left(r-7\right)}-\frac{6}{r-7}
Factor r^{2}-16r+63.
\frac{10r-1}{\left(r-9\right)\left(r-7\right)}-\frac{6\left(r-9\right)}{\left(r-9\right)\left(r-7\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(r-9\right)\left(r-7\right) and r-7 is \left(r-9\right)\left(r-7\right). Multiply \frac{6}{r-7} times \frac{r-9}{r-9}.
\frac{10r-1-6\left(r-9\right)}{\left(r-9\right)\left(r-7\right)}
Since \frac{10r-1}{\left(r-9\right)\left(r-7\right)} and \frac{6\left(r-9\right)}{\left(r-9\right)\left(r-7\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{10r-1-6r+54}{\left(r-9\right)\left(r-7\right)}
Do the multiplications in 10r-1-6\left(r-9\right).
\frac{4r+53}{\left(r-9\right)\left(r-7\right)}
Combine like terms in 10r-1-6r+54.
\frac{4r+53}{r^{2}-16r+63}
Expand \left(r-9\right)\left(r-7\right).
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}