To simplify the expression, we need to factor each of the numerators and denominators and then cancel any common factors.
First, let's factor the numerator and denominator of the first rational expression:
x^2 - 11x + 30 = (x - 5)(x - 6)
x^2 - 25 = (x - 5)(x + 5)
Now, let's factor the numerator and denominator of the second rational expression:
x^2 + 8x + 15 = (x + 3)(x + 5)
x^2 - 3x - 18 = (x - 6)(x + 3)
Multiplying the two rational expressions together, we get:
((x - 5)(x - 6) / (x - 5)(x + 5)) * ((x + 3)(x + 5) / (x - 6)(x + 3))
Next, we cancel out the common factors:
(x - 5) from the first numerator and first denominator,
(x - 6) from the first numerator and second denominator,
(x + 3) from the second numerator and second denominator,
and (x + 5) from the first and second denominator.
After canceling out these common factors, we are left with:
1 / (x + 5)
So, the simplified rational expression is 1 / (x + 5).
Restriction on the variable:
The variable x cannot be equal to -5, as it would make the denominator zero, which is not allowed in a rational expression.
Multiply and then simplify the rational expression. State any restrictions on the variable.
x^2-11x+30/x^2-25 * x^2+8x+15/x^2-3x-18
1 answer
1 answer