Evaluate
\frac{8x^{2}-13x-12}{\left(2x-1\right)\left(3x+4\right)}
Expand
\frac{8x^{2}-13x-12}{\left(2x-1\right)\left(3x+4\right)}
Graph
Quiz
Polynomial
\frac { 2 x } { 3 x + 4 } + \frac { 4 x ^ { 2 } - 11 x - 12 } { 6 x ^ { 2 } + 5 x - 4 }
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\frac{2x}{3x+4}+\frac{4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
Factor 6x^{2}+5x-4.
\frac{2x\left(2x-1\right)}{\left(2x-1\right)\left(3x+4\right)}+\frac{4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x+4 and \left(2x-1\right)\left(3x+4\right) is \left(2x-1\right)\left(3x+4\right). Multiply \frac{2x}{3x+4} times \frac{2x-1}{2x-1}.
\frac{2x\left(2x-1\right)+4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
Since \frac{2x\left(2x-1\right)}{\left(2x-1\right)\left(3x+4\right)} and \frac{4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-2x+4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
Do the multiplications in 2x\left(2x-1\right)+4x^{2}-11x-12.
\frac{8x^{2}-13x-12}{\left(2x-1\right)\left(3x+4\right)}
Combine like terms in 4x^{2}-2x+4x^{2}-11x-12.
\frac{8x^{2}-13x-12}{6x^{2}+5x-4}
Expand \left(2x-1\right)\left(3x+4\right).
\frac{2x}{3x+4}+\frac{4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
Factor 6x^{2}+5x-4.
\frac{2x\left(2x-1\right)}{\left(2x-1\right)\left(3x+4\right)}+\frac{4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x+4 and \left(2x-1\right)\left(3x+4\right) is \left(2x-1\right)\left(3x+4\right). Multiply \frac{2x}{3x+4} times \frac{2x-1}{2x-1}.
\frac{2x\left(2x-1\right)+4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
Since \frac{2x\left(2x-1\right)}{\left(2x-1\right)\left(3x+4\right)} and \frac{4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}-2x+4x^{2}-11x-12}{\left(2x-1\right)\left(3x+4\right)}
Do the multiplications in 2x\left(2x-1\right)+4x^{2}-11x-12.
\frac{8x^{2}-13x-12}{\left(2x-1\right)\left(3x+4\right)}
Combine like terms in 4x^{2}-2x+4x^{2}-11x-12.
\frac{8x^{2}-13x-12}{6x^{2}+5x-4}
Expand \left(2x-1\right)\left(3x+4\right).
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