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5 problems similar to:
\frac{ 2 { x }^{ 2 } }{ 2 { x }^{ 2 } -3x } - \frac{ 9 }{ 6x-9 }
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\frac{2x^{2}}{x\left(2x-3\right)}-\frac{9}{6x-9}
Factor the expressions that are not already factored in \frac{2x^{2}}{2x^{2}-3x}.
\frac{2x}{2x-3}-\frac{9}{6x-9}
Cancel out x in both numerator and denominator.
\frac{2x}{2x-3}-\frac{9}{3\left(2x-3\right)}
Factor 6x-9.
\frac{3\times 2x}{3\left(2x-3\right)}-\frac{9}{3\left(2x-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3 and 3\left(2x-3\right) is 3\left(2x-3\right). Multiply \frac{2x}{2x-3} times \frac{3}{3}.
\frac{3\times 2x-9}{3\left(2x-3\right)}
Since \frac{3\times 2x}{3\left(2x-3\right)} and \frac{9}{3\left(2x-3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x-9}{3\left(2x-3\right)}
Do the multiplications in 3\times 2x-9.
\frac{3\left(2x-3\right)}{3\left(2x-3\right)}
Factor the expressions that are not already factored in \frac{6x-9}{3\left(2x-3\right)}.
1
Cancel out 3\left(2x-3\right) in both numerator and denominator.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}