Question

x^2 -1 over x^2 - 5x - 6 divided by 5x + 25 over x-6

Answer 1

express in simplest form

Answer 2

To divide the given expression

(x^2 - 1) / (x^2 - 5x - 6) ÷ (5x + 25) / (x - 6)

We first need to simplify the expression using the rules of fractions and division.

1. Factor both the numerator and denominator of the first fraction:
Numerator: x^2 - 1 = (x - 1)(x + 1)
Denominator: x^2 - 5x - 6 = (x - 6)(x + 1)

2. Rewrite the expression with factored terms:
[(x - 1)(x + 1) / (x - 6)(x + 1)] ÷ [(5x + 25) / (x - 6)]

3. Factor out common factors and simplify the division:
[(x - 1) / (x - 6)] ÷ [(5(x + 5)) / (x - 6)]

4. Invert the second fraction and multiply:
[(x - 1) / (x - 6)] * [(x - 6) / (5(x + 5))]
= (x - 1)(x - 6) / 5(x + 5)

5. Further simplify the expression by expanding the numerator:
= (x^2 - 7x + 6) / (5x + 25)
= (x - 6)(x - 1) / 5(x + 5)

Therefore, the simplified expression after division is:

(x^2 - 7x + 6) / (5x + 25) or (x - 6)(x - 1) / 5(x + 5)

Answer 3

To express the given expression in simplest form, you can factor out the numerator and denominator as follows:

(x^2 - 7x + 6) = (x - 6)(x - 1)
(5x + 25) = 5(x + 5)

Therefore, the expression can be rewritten as follows:

(x - 6)(x - 1) / 5(x + 5)

This is the simplest form of the expression after division.