(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

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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

Adam

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!

Nov 23, 2019 • Reply

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Chris Lele