Evaluate
\frac{\left(2x+3\right)\left(2x+5\right)}{\left(x-4\right)\left(x+1\right)}
Expand
\frac{4x^{2}+16x+15}{\left(x-4\right)\left(x+1\right)}
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\frac{2x+3}{x-4}+\frac{\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
Divide \frac{2x+3}{x-4} by \frac{x+1}{x+4} by multiplying \frac{2x+3}{x-4} by the reciprocal of \frac{x+1}{x+4}.
\frac{\left(2x+3\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}+\frac{\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+1\right) is \left(x-4\right)\left(x+1\right). Multiply \frac{2x+3}{x-4} times \frac{x+1}{x+1}.
\frac{\left(2x+3\right)\left(x+1\right)+\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
Since \frac{\left(2x+3\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)} and \frac{\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+2x+3x+3+2x^{2}+8x+3x+12}{\left(x-4\right)\left(x+1\right)}
Do the multiplications in \left(2x+3\right)\left(x+1\right)+\left(2x+3\right)\left(x+4\right).
\frac{4x^{2}+16x+15}{\left(x-4\right)\left(x+1\right)}
Combine like terms in 2x^{2}+2x+3x+3+2x^{2}+8x+3x+12.
\frac{4x^{2}+16x+15}{x^{2}-3x-4}
Expand \left(x-4\right)\left(x+1\right).
\frac{2x+3}{x-4}+\frac{\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
Divide \frac{2x+3}{x-4} by \frac{x+1}{x+4} by multiplying \frac{2x+3}{x-4} by the reciprocal of \frac{x+1}{x+4}.
\frac{\left(2x+3\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}+\frac{\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+1\right) is \left(x-4\right)\left(x+1\right). Multiply \frac{2x+3}{x-4} times \frac{x+1}{x+1}.
\frac{\left(2x+3\right)\left(x+1\right)+\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
Since \frac{\left(2x+3\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)} and \frac{\left(2x+3\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+2x+3x+3+2x^{2}+8x+3x+12}{\left(x-4\right)\left(x+1\right)}
Do the multiplications in \left(2x+3\right)\left(x+1\right)+\left(2x+3\right)\left(x+4\right).
\frac{4x^{2}+16x+15}{\left(x-4\right)\left(x+1\right)}
Combine like terms in 2x^{2}+2x+3x+3+2x^{2}+8x+3x+12.
\frac{4x^{2}+16x+15}{x^{2}-3x-4}
Expand \left(x-4\right)\left(x+1\right).
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