Evaluate
\frac{56q^{2}+43q+24}{2\left(q+3\right)\left(8q+5\right)}
Factor
\frac{56q^{2}+43q+24}{2\left(q+3\right)\left(8q+5\right)}
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\frac{7q}{2\left(q+3\right)}+\frac{4}{8q+5}
Factor 2q+6.
\frac{7q\left(8q+5\right)}{2\left(q+3\right)\left(8q+5\right)}+\frac{4\times 2\left(q+3\right)}{2\left(q+3\right)\left(8q+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(q+3\right) and 8q+5 is 2\left(q+3\right)\left(8q+5\right). Multiply \frac{7q}{2\left(q+3\right)} times \frac{8q+5}{8q+5}. Multiply \frac{4}{8q+5} times \frac{2\left(q+3\right)}{2\left(q+3\right)}.
\frac{7q\left(8q+5\right)+4\times 2\left(q+3\right)}{2\left(q+3\right)\left(8q+5\right)}
Since \frac{7q\left(8q+5\right)}{2\left(q+3\right)\left(8q+5\right)} and \frac{4\times 2\left(q+3\right)}{2\left(q+3\right)\left(8q+5\right)} have the same denominator, add them by adding their numerators.
\frac{56q^{2}+35q+8q+24}{2\left(q+3\right)\left(8q+5\right)}
Do the multiplications in 7q\left(8q+5\right)+4\times 2\left(q+3\right).
\frac{56q^{2}+43q+24}{2\left(q+3\right)\left(8q+5\right)}
Combine like terms in 56q^{2}+35q+8q+24.
\frac{56q^{2}+43q+24}{16q^{2}+58q+30}
Expand 2\left(q+3\right)\left(8q+5\right).
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