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