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\frac{\frac{36x}{x\left(x-4\right)}-\frac{36\left(x-4\right)}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and x is x\left(x-4\right). Multiply \frac{36}{x-4} times \frac{x}{x}. Multiply \frac{36}{x} times \frac{x-4}{x-4}.
\frac{\frac{36x-36\left(x-4\right)}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
Since \frac{36x}{x\left(x-4\right)} and \frac{36\left(x-4\right)}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{36x-36x+144}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
Do the multiplications in 36x-36\left(x-4\right).
\frac{\frac{144}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
Combine like terms in 36x-36x+144.
\frac{\frac{144}{x\left(x-4\right)}}{\frac{29}{x-4}}
Since \frac{30}{x-4} and \frac{1}{x-4} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 30 to get 29.
\frac{144\left(x-4\right)}{x\left(x-4\right)\times 29}
Divide \frac{144}{x\left(x-4\right)} by \frac{29}{x-4} by multiplying \frac{144}{x\left(x-4\right)} by the reciprocal of \frac{29}{x-4}.
\frac{144}{29x}
Cancel out x-4 in both numerator and denominator.
\frac{\frac{36x}{x\left(x-4\right)}-\frac{36\left(x-4\right)}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and x is x\left(x-4\right). Multiply \frac{36}{x-4} times \frac{x}{x}. Multiply \frac{36}{x} times \frac{x-4}{x-4}.
\frac{\frac{36x-36\left(x-4\right)}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
Since \frac{36x}{x\left(x-4\right)} and \frac{36\left(x-4\right)}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{36x-36x+144}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
Do the multiplications in 36x-36\left(x-4\right).
\frac{\frac{144}{x\left(x-4\right)}}{\frac{30}{x-4}-\frac{1}{x-4}}
Combine like terms in 36x-36x+144.
\frac{\frac{144}{x\left(x-4\right)}}{\frac{29}{x-4}}
Since \frac{30}{x-4} and \frac{1}{x-4} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 30 to get 29.
\frac{144\left(x-4\right)}{x\left(x-4\right)\times 29}
Divide \frac{144}{x\left(x-4\right)} by \frac{29}{x-4} by multiplying \frac{144}{x\left(x-4\right)} by the reciprocal of \frac{29}{x-4}.
\frac{144}{29x}
Cancel out x-4 in both numerator and denominator.