Evaluate
\frac{16x^{2}+25x+35}{4x+5}
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\frac{16x^{2}+25x+35}{4x+5}
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4x+\frac{5\left(4x^{2}+23x-35\right)}{16x^{2}-25}
Divide 5 by \frac{16x^{2}-25}{4x^{2}+23x-35} by multiplying 5 by the reciprocal of \frac{16x^{2}-25}{4x^{2}+23x-35}.
4x+\frac{5\left(4x-5\right)\left(x+7\right)}{\left(4x-5\right)\left(4x+5\right)}
Factor the expressions that are not already factored in \frac{5\left(4x^{2}+23x-35\right)}{16x^{2}-25}.
4x+\frac{5\left(x+7\right)}{4x+5}
Cancel out 4x-5 in both numerator and denominator.
\frac{4x\left(4x+5\right)}{4x+5}+\frac{5\left(x+7\right)}{4x+5}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{4x+5}{4x+5}.
\frac{4x\left(4x+5\right)+5\left(x+7\right)}{4x+5}
Since \frac{4x\left(4x+5\right)}{4x+5} and \frac{5\left(x+7\right)}{4x+5} have the same denominator, add them by adding their numerators.
\frac{16x^{2}+20x+5x+35}{4x+5}
Do the multiplications in 4x\left(4x+5\right)+5\left(x+7\right).
\frac{16x^{2}+25x+35}{4x+5}
Combine like terms in 16x^{2}+20x+5x+35.
4x+\frac{5\left(4x^{2}+23x-35\right)}{16x^{2}-25}
Divide 5 by \frac{16x^{2}-25}{4x^{2}+23x-35} by multiplying 5 by the reciprocal of \frac{16x^{2}-25}{4x^{2}+23x-35}.
4x+\frac{5\left(4x-5\right)\left(x+7\right)}{\left(4x-5\right)\left(4x+5\right)}
Factor the expressions that are not already factored in \frac{5\left(4x^{2}+23x-35\right)}{16x^{2}-25}.
4x+\frac{5\left(x+7\right)}{4x+5}
Cancel out 4x-5 in both numerator and denominator.
\frac{4x\left(4x+5\right)}{4x+5}+\frac{5\left(x+7\right)}{4x+5}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{4x+5}{4x+5}.
\frac{4x\left(4x+5\right)+5\left(x+7\right)}{4x+5}
Since \frac{4x\left(4x+5\right)}{4x+5} and \frac{5\left(x+7\right)}{4x+5} have the same denominator, add them by adding their numerators.
\frac{16x^{2}+20x+5x+35}{4x+5}
Do the multiplications in 4x\left(4x+5\right)+5\left(x+7\right).
\frac{16x^{2}+25x+35}{4x+5}
Combine like terms in 16x^{2}+20x+5x+35.
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Limits
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