Multiply. State any restrictions on the variable.
(x^2-5x+6)/(x^2-4) * (x^2+3x+2)/(x^2-2x-3)
((x-2)(x-3))/((x-2)(x+2)) * ((x+1)(x+2))/((x+1)(x-3))
Restrictions: x cannot be equal to 2, -2, -1, or 3 to avoid division by zero.
Please show step by step.
Sure! Here are the step by step calculations:
1. Simplify the first fraction: (x^2-5x+6)/(x^2-4)
Factor the numerator and denominator:
(x^2-5x+6) = (x-2)(x-3)
(x^2-4) = (x+2)(x-2)
So the first fraction becomes:
(x-2)(x-3) / (x-2)(x+2)
2. Simplify the second fraction: (x^2+3x+2)/(x^2-2x-3)
Factor the numerator and denominator:
(x^2+3x+2) = (x+1)(x+2)
(x^2-2x-3) = (x+1)(x-3)
So the second fraction becomes:
(x+1)(x+2) / (x+1)(x-3)
3. Multiply the two simplified fractions:
((x-2)(x-3) / (x-2)(x+2)) * ((x+1)(x+2) / (x+1)(x-3))
= (x-2)(x-3)(x+1)(x+2) / (x-2)(x+2)(x+1)(x-3)
4. Cancel out the common factors:
= (x+1)(x+2) / (x+2)(x-3)
So, the final simplified expression is:
(x+1)(x+2) / (x+2)(x-3)
And the restrictions on the variable are:
x cannot be equal to 2, -2, -1, or 3.