What is the quotient in simplest form? State any restrictions on the variable.
x+2/x-1 divide x+4/x^2+4x-5
The quotient is:
(x+2)/(x-1) ÷ (x+4)/(x^2+4x-5)
To simplify, we can rewrite the division as multiplication by the reciprocal of the second fraction:
(x+2)/(x-1) * (x^2+4x-5)/(x+4)
Now, we can simplify by factoring:
x+2 = x+2
x-1 = x-1
x^2+4x-5 = (x+5)(x-1)
x+4 = x+4
(x+2)/(x-1) * (x^2+4x-5)/(x+4) = (x+2)(x+5)/(x+4)
Therefore, the quotient in simplest form is: (x+2)(x+5)/(x+4)
Restrictions:
- The denominator of the original fraction, (x-1) should not equal 0, so x cannot be equal to 1.
- The denominator of the simplified fraction, (x+4) should not equal 0, so x cannot be equal to -4.