Evaluate
\frac{11+37x-65x^{2}}{8-11x}
Expand
\frac{11+37x-65x^{2}}{8-11x}
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\frac{\left(6x+1\right)\left(-11x+8\right)}{-11x+8}+\frac{x^{2}+3}{-11x+8}
To add or subtract expressions, expand them to make their denominators the same. Multiply 6x+1 times \frac{-11x+8}{-11x+8}.
\frac{\left(6x+1\right)\left(-11x+8\right)+x^{2}+3}{-11x+8}
Since \frac{\left(6x+1\right)\left(-11x+8\right)}{-11x+8} and \frac{x^{2}+3}{-11x+8} have the same denominator, add them by adding their numerators.
\frac{-66x^{2}+48x-11x+8+x^{2}+3}{-11x+8}
Do the multiplications in \left(6x+1\right)\left(-11x+8\right)+x^{2}+3.
\frac{-65x^{2}+37x+11}{-11x+8}
Combine like terms in -66x^{2}+48x-11x+8+x^{2}+3.
\frac{\left(6x+1\right)\left(-11x+8\right)}{-11x+8}+\frac{x^{2}+3}{-11x+8}
To add or subtract expressions, expand them to make their denominators the same. Multiply 6x+1 times \frac{-11x+8}{-11x+8}.
\frac{\left(6x+1\right)\left(-11x+8\right)+x^{2}+3}{-11x+8}
Since \frac{\left(6x+1\right)\left(-11x+8\right)}{-11x+8} and \frac{x^{2}+3}{-11x+8} have the same denominator, add them by adding their numerators.
\frac{-66x^{2}+48x-11x+8+x^{2}+3}{-11x+8}
Do the multiplications in \left(6x+1\right)\left(-11x+8\right)+x^{2}+3.
\frac{-65x^{2}+37x+11}{-11x+8}
Combine like terms in -66x^{2}+48x-11x+8+x^{2}+3.
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}