Question

build the fraction into an equivalent with the indicated denomintor 2y/x; x^2 + x

Answer 1

The current denominator is x, but we want x^2+x. We can factor x^2+x into x(x+1). So we're missing an "x+1" term from the denominator. This means that we have to multiply BOTH the numerator AND the denominator by x+1 to get to our desired goal. Do this to get (2y/x)((x+1)/(x+1)) = (2y(x+1))/(x(x+1)) = (2xy+2y)/(x^2+x)