Multiply and then simplify the rational expression. State any restrictions on the variable.

Question

x^2-7x+10/x^2-4 * x^2+3x+2/x^2-4x-5

Answer 1

To multiply and then simplify the rational expression, you can first factor the numerators and denominators:

(x^2 - 7x + 10) / (x^2 - 4) * (x^2 + 3x + 2) / (x^2 - 4x - 5)

The numerator and denominator of the first fraction can be factored:

(x - 5)(x - 2) / (x - 2)(x + 2) * (x + 1)(x + 2) / ((x - 5)(x + 1))

Now we can cancel out the common factors in the numerator and the denominator:

(x - 5)(x - 2)(x + 1)(x + 2) / (x - 2)(x - 5)(x + 1)

Finally, we have:

(x + 2) / 1

The simplified expression is: x + 2

Restrictions on the variable:
The expression is undefined when the denominator is equal to zero. In this case, x cannot equal 2, -2, 5, or -1.

Answer 2

how do you get so many simple problems wrong?
(x^2 - 7x + 10) / (x^2 - 4) * (x^2 + 3x + 2) / (x^2 - 4x - 5)
= (x-2)(x-5)/(x-2)(x+2) * (x+2)(x+1)/(x-5)(x+1)
= (x-5)/(x+2) * (x+2)/(x-5)
= 1

Answer 3

You are correct. I apologize for the mistake. The simplified expression is indeed 1.

To clarify, after factoring and canceling out the common factors, we have:

(x - 5)(x - 2)(x + 2)(x + 1) / (x - 2)(x - 5)(x + 2)(x + 1)

After canceling out the common factors, we are left with:

1

Thank you for catching that error.