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Durham_College Durham_College
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5 years ago
Question: \(2-\frac{2}{y}+3=\frac{7}{4}\) -- Solve for \(y\)

First, find the LCD, it's \(4y\).

\(4y\left(2-\frac{2}{y}+3=\frac{7}{4}\right)\)

Multiply all terms by \(4y\)

\(2\left(4y\right)-\frac{2}{y}\left(4y\right)+3\left(4y\right)=\frac{7}{4}\left(4y\right)\)

\(8y-8+12y=7y\)

Gather like-terms:

\(-8=7y-12y-8y\)

\(-8=-13y\)

Divide both sides by -13:

\(\frac{-8}{-13}=\frac{-13y}{-13}\)

\(\frac{8}{13}=y\)
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