Evaluate
\frac{\left(3-5x\right)\left(3x-5\right)}{6\left(1-x\right)^{3}}
Expand
\frac{15x^{2}-34x+15}{6\left(x-1\right)^{3}}
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\frac{5\times 3\left(x-1\right)^{2}}{6\left(x-1\right)^{3}}+\frac{-2\times 2x}{6\left(x-1\right)^{3}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-1\right) and 3\left(1-x\right)^{3} is 6\left(x-1\right)^{3}. Multiply \frac{5}{2\left(x-1\right)} times \frac{3\left(x-1\right)^{2}}{3\left(x-1\right)^{2}}. Multiply \frac{2x}{3\left(1-x\right)^{3}} times \frac{-2}{-2}.
\frac{5\times 3\left(x-1\right)^{2}-2\times 2x}{6\left(x-1\right)^{3}}
Since \frac{5\times 3\left(x-1\right)^{2}}{6\left(x-1\right)^{3}} and \frac{-2\times 2x}{6\left(x-1\right)^{3}} have the same denominator, add them by adding their numerators.
\frac{15x^{2}-30x+15-4x}{6\left(x-1\right)^{3}}
Do the multiplications in 5\times 3\left(x-1\right)^{2}-2\times 2x.
\frac{15x^{2}-34x+15}{6\left(x-1\right)^{3}}
Combine like terms in 15x^{2}-30x+15-4x.
\frac{15x^{2}-34x+15}{6x^{3}-18x^{2}+18x-6}
Expand 6\left(x-1\right)^{3}.
\frac{5\times 3\left(x-1\right)^{2}}{6\left(x-1\right)^{3}}+\frac{-2\times 2x}{6\left(x-1\right)^{3}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-1\right) and 3\left(1-x\right)^{3} is 6\left(x-1\right)^{3}. Multiply \frac{5}{2\left(x-1\right)} times \frac{3\left(x-1\right)^{2}}{3\left(x-1\right)^{2}}. Multiply \frac{2x}{3\left(1-x\right)^{3}} times \frac{-2}{-2}.
\frac{5\times 3\left(x-1\right)^{2}-2\times 2x}{6\left(x-1\right)^{3}}
Since \frac{5\times 3\left(x-1\right)^{2}}{6\left(x-1\right)^{3}} and \frac{-2\times 2x}{6\left(x-1\right)^{3}} have the same denominator, add them by adding their numerators.
\frac{15x^{2}-30x+15-4x}{6\left(x-1\right)^{3}}
Do the multiplications in 5\times 3\left(x-1\right)^{2}-2\times 2x.
\frac{15x^{2}-34x+15}{6\left(x-1\right)^{3}}
Combine like terms in 15x^{2}-30x+15-4x.
\frac{15x^{2}-34x+15}{6x^{3}-18x^{2}+18x-6}
Expand 6\left(x-1\right)^{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}