Evaluate
\frac{61x^{5}+244x^{4}+13x+12}{2x\left(61x^{4}+3\right)}
Expand
\frac{61x^{5}+244x^{4}+13x+12}{2x\left(61x^{4}+3\right)}
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\frac{5\times 2x}{2x\left(61x^{4}+3\right)}+\frac{\left(x+4\right)\left(61x^{4}+3\right)}{2x\left(61x^{4}+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 61x^{4}+3 and 2x is 2x\left(61x^{4}+3\right). Multiply \frac{5}{61x^{4}+3} times \frac{2x}{2x}. Multiply \frac{x+4}{2x} times \frac{61x^{4}+3}{61x^{4}+3}.
\frac{5\times 2x+\left(x+4\right)\left(61x^{4}+3\right)}{2x\left(61x^{4}+3\right)}
Since \frac{5\times 2x}{2x\left(61x^{4}+3\right)} and \frac{\left(x+4\right)\left(61x^{4}+3\right)}{2x\left(61x^{4}+3\right)} have the same denominator, add them by adding their numerators.
\frac{10x+61x^{5}+3x+244x^{4}+12}{2x\left(61x^{4}+3\right)}
Do the multiplications in 5\times 2x+\left(x+4\right)\left(61x^{4}+3\right).
\frac{13x+61x^{5}+244x^{4}+12}{2x\left(61x^{4}+3\right)}
Combine like terms in 10x+61x^{5}+3x+244x^{4}+12.
\frac{13x+61x^{5}+244x^{4}+12}{122x^{5}+6x}
Expand 2x\left(61x^{4}+3\right).
\frac{5\times 2x}{2x\left(61x^{4}+3\right)}+\frac{\left(x+4\right)\left(61x^{4}+3\right)}{2x\left(61x^{4}+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 61x^{4}+3 and 2x is 2x\left(61x^{4}+3\right). Multiply \frac{5}{61x^{4}+3} times \frac{2x}{2x}. Multiply \frac{x+4}{2x} times \frac{61x^{4}+3}{61x^{4}+3}.
\frac{5\times 2x+\left(x+4\right)\left(61x^{4}+3\right)}{2x\left(61x^{4}+3\right)}
Since \frac{5\times 2x}{2x\left(61x^{4}+3\right)} and \frac{\left(x+4\right)\left(61x^{4}+3\right)}{2x\left(61x^{4}+3\right)} have the same denominator, add them by adding their numerators.
\frac{10x+61x^{5}+3x+244x^{4}+12}{2x\left(61x^{4}+3\right)}
Do the multiplications in 5\times 2x+\left(x+4\right)\left(61x^{4}+3\right).
\frac{13x+61x^{5}+244x^{4}+12}{2x\left(61x^{4}+3\right)}
Combine like terms in 10x+61x^{5}+3x+244x^{4}+12.
\frac{13x+61x^{5}+244x^{4}+12}{122x^{5}+6x}
Expand 2x\left(61x^{4}+3\right).
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