Math CentralQuandaries & Queries


Question from AMANDA, a parent:

15 - (5-x)/ x = 30

I thought you had to multiply both sides by x in order to remove the fraction?

15x - 5x - x2 = 30x

then combine 10x - x2 = 30x

-x2 =20x

then take the sqrt of each side...

what am I doing wrong??

Hi Amanda,

Multiplying $\frac{5-x}{x}$ by $x$ gives

\[x \times \frac{5-x}{x}.\]

The $x$ multiplier and the $x$ in the denominator cancel and hence

\[x \times \frac{5-x}{x} = 5-x.\]

Hence multiplying both sides of your equation by $x$ yields

\[15x - (5-x) = 30x\]

Solve for $x.$ Make sure you verify your answer,

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