what is the quotient of. please show step by step
x+4/x-1 / x^2+x/x-1
as with any fraction divisor, multiply by its reciprocal. That gives you
(x+4)/(x-1) * (x-1)(x^2+x)
The x-1 factors cancel, so ...
To find the quotient of the given expression, (x+4)/(x-1) divided by (x^2+x)/(x-1), we proceed with the following steps:
Step 1: Factor the expressions, if possible.
(x+4)/(x-1) can't be simplified further.
(x^2+x) can be factored as x(x+1).
Step 2: Rewrite the division as multiplication by the reciprocal.
The quotient becomes: (x+4)/(x-1) * (x-1)/(x^2+x)
Step 3: Simplify the expression by canceling out common factors.
The (x-1) factors cancel out in the numerator and denominator:
(x+4)/(x^2+x)
Step 4: Simplify the expression further, if possible.
The denominator cannot be factored further.
Thus, the quotient of (x+4)/(x-1) divided by (x^2+x)/(x-1) is (x+4)/(x^2+x).