Identify the equivalent expression in the equation, 1/x^2-x + 1/x = 5/x^2-x, and demonstrate multiplying by the common denominator.

Answer 1

The equivalent expression in the equation 1/x^2 - x + 1/x = 5/x^2 - x can be found by multiplying both sides of the equation by (x^2 - x).

(x^2 - x) * (1/x^2 - x) + (x^2 - x) * (1/x) = (x^2 - x) * (5/x^2 - x)

Expanding each term:

1 - x(x^2 - x) + (x^2 - x)(1/x) = 5(x^2 - x)

1 - x^3 + x^2 + x - x^2 + x = 5x^2 - 5x

Simplifying:

1 + x^2 + x = 5x^2 - 5x

The equivalent expression is 1 + x^2 + x = 5x^2 - 5x.