Source: Official Guide Revised GRE 1st Ed. Part 8; Section 6; #8

3

# (1-x)/(x-1)=1/x

(1-x)/(x-1)=1/x Quantity A : x Quantity B : -1/2 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

### 2 Explanations

1

Melanie Sharif

I thought that cross-multiplication was not allowed if we are unsure if a fraction is positive or negative?

Could you also explain how the ETS book finds "x(x+1)" to be the common denominator that can be multiplied by both sides of the equation to reduce the fraction?

Nov 17, 2019 • Comment

Hey Melanie,
Cross multiplication is always allowed for equations. For *inequalities* the rules are slightly different. With inequalities, we can't cross multiply using a variable if we don't know the sign of the variable. But with equations we can always cross multiply.
And the common denominator should be x(x-1), not x(x+1). You can multiply both sides by x(x-1) to eliminate the fractions.
Hope that helps!

5 Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment