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\frac{\left(x+1\right)\times 2}{4\left(x-5\right)}
Divide \frac{x+1}{4} by \frac{x-5}{2} by multiplying \frac{x+1}{4} by the reciprocal of \frac{x-5}{2}.
\frac{x+1}{2\left(x-5\right)}
Cancel out 2 in both numerator and denominator.
\frac{x+1}{2x-10}
Use the distributive property to multiply 2 by x-5.
\frac{\left(x+1\right)\times 2}{4\left(x-5\right)}
Divide \frac{x+1}{4} by \frac{x-5}{2} by multiplying \frac{x+1}{4} by the reciprocal of \frac{x-5}{2}.
\frac{x+1}{2\left(x-5\right)}
Cancel out 2 in both numerator and denominator.
\frac{x+1}{2x-10}
Use the distributive property to multiply 2 by x-5.