Question

Divide 4/x-4 ÷ 12/2x-8

Answer 1

To divide rational expressions, first rewrite division as multiplication by the reciprocal. Then, simplify the expression by canceling out common factors. Finally, multiply the numerators and denominators.

Step-by-step explanation:

To divide rational expressions, we first need to identify that division can be rewritten as multiplication by the reciprocal.

Thus, the expression becomes:

4/x-4 * 2x-8/12

Simplifying further, we can cancel out common factors:

1. 
   
3. The factor of 4 in the numerator cancels with the factor of 4 in the denominator.
4. 
   
6. The factor of (x-4) in the numerator cancels with the factor of (x-4) in the denominator.
7. 
   
9. The factor of 2 in the numerator cancels with the factor of 2 in the denominator.

After canceling out these factors, we are left with:

1/(x-4) * (2x-8)/3

Further simplification can be done by multiplying the numerators and denominators together:

(2x-8)/(3(x-4))

Thus, the simplified expression is (2x-8)/(3(x-4)).

Learn more about Dividing rational expressions