Question

Divide.

Start Fraction x squared plus 9 x plus 20 over x squared minus 25 End Fraction divided by Start Fraction x plus 4 over x minus 4 End Fraction

Answer 1

To divide two fractions, we must multiply the first fraction by the reciprocal of the second fraction.

First, factor the quadratic expressions in the numerator and denominator of the first fraction:

x^2 + 9x + 20 = (x + 4)(x + 5)
x^2 - 25 = (x + 5)(x - 5)

Now, we have:

[(x + 4)(x + 5) / (x + 5)(x - 5)] ÷ [x + 4 / x - 4]

To simplify, we can cancel out common factors:

[(x + 4) / (x - 5)] ÷ [x + 4 / x - 4]

Now, multiply the first fraction by the reciprocal of the second fraction:

(x + 4)(x - 4) / (x - 5)(x + 4)

Simplify the expression further:

(x - 4) / (x - 5)