Question

Simplify the expression. $$\frac{x}{8-2 x} \div \frac{2 x}{4-x}$$

Short answer

The simplified form of \(\frac{x}{8-2x} \div \frac{2x}{4-x}\) is \(-1\)

Step-by-step solution

Take Reciprocal

Change the division sign into a multiplication and take reciprocal of the second fraction: \(\frac{x}{8-2x} × \frac{4-x}{2x}\)

Distribute Negative Sign

After taking the reciprocal of the second fraction, distribute negative sign in the denominator of the first fraction and in the numerator of the second fraction: \(\frac{x}{-2x+8} × \frac{-x+4}{2x}\)

Factorize

In both fractions, factor out a -1 from the numerator of second fraction and denominator of the first fraction: \(\frac{x}{2(-x+4)} × \frac{-1(x-4)}{2x}\)

Simplify

Simplify by cancelling out the common factors: \(-1\)

Interpret the Result

The result can be interpreted as the simplified form of the given expression