Question

Identify the equivalent expression in the equation 1x2−x+1x=5x2−x
and demonstrate multiplying by the common denominator.(1 point)

x(1x2−x)+x(1x)=x(5x2−x)


(x−1)(1x2−x)+(x−1)(1x)=(x−1)(5x2−x)


(x2−x)(1x2−x)+(x2−x)(1x)=(x2−x)(5x2−x)


x2(1x2−x)+x2(1x)=x2(5x2−x)

Answer 1

The common denominator is x^2 − x = x(x−1). Multiplying both sides by x^2 − x gives the equivalent equation

(x^2 − x)(1/(x^2 − x)) + (x^2 − x)(1/x) = (x^2 − x)(5/(x^2 − x)),

so the correct choice is the third one.

Simplify:
1 + (x^2 − x)/x = 5
1 + (x − 1) = 5
x = 5,

with domain restrictions x ≠ 0 and x ≠ 1.