Evaluate
\frac{3x\left(7a-4\right)}{9a^{2}-16}
|a|\neq \frac{4}{3}
Factor
\frac{3x\left(7a-4\right)}{9a^{2}-16}
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\frac{5x\left(3a-4\right)}{\left(3a-4\right)\left(3a+4\right)}+\frac{2x\left(3a+4\right)}{\left(3a-4\right)\left(3a+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a+4 and 3a-4 is \left(3a-4\right)\left(3a+4\right). Multiply \frac{5x}{3a+4} times \frac{3a-4}{3a-4}. Multiply \frac{2x}{3a-4} times \frac{3a+4}{3a+4}.
\frac{5x\left(3a-4\right)+2x\left(3a+4\right)}{\left(3a-4\right)\left(3a+4\right)}
Since \frac{5x\left(3a-4\right)}{\left(3a-4\right)\left(3a+4\right)} and \frac{2x\left(3a+4\right)}{\left(3a-4\right)\left(3a+4\right)} have the same denominator, add them by adding their numerators.
\frac{15xa-20x+6xa+8x}{\left(3a-4\right)\left(3a+4\right)}
Do the multiplications in 5x\left(3a-4\right)+2x\left(3a+4\right).
\frac{21xa-12x}{\left(3a-4\right)\left(3a+4\right)}
Combine like terms in 15xa-20x+6xa+8x.
\frac{21xa-12x}{9a^{2}-16}
Expand \left(3a-4\right)\left(3a+4\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}