 # To clear the following equation of fractions, by what should both sides be multi Josalynn 2021-09-30 Answered
To clear the following equation of fractions, by what should both sides be multiplied?
$$\displaystyle{\frac{{{7}}}{{{10}}}}+{y}={\frac{{{2}{y}-{38}}}{{{5}{y}-{25}}}}$$

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Step 1
The equation is $$\displaystyle{\frac{{{7}}}{{{10}}}}+{y}={\frac{{{2}{y}-{38}}}{{{5}{y}-{25}}}}$$.
An expression is to be multiplied such that there is no fraction on both sides and then the equation can be simplified.
Step 2
The equation is $$\displaystyle{\frac{{{7}}}{{{10}}}}+{y}={\frac{{{2}{y}-{38}}}{{{5}{y}-{25}}}}$$
Multiply $$\displaystyle{10}{\left({5}{y}-{25}\right)}$$ on both sides of the equation.
$$\displaystyle{\frac{{{7}}}{{{10}}}}+{y}={\frac{{{2}{y}-{38}}}{{{5}{y}-{25}}}}$$
$$\displaystyle{10}{\left({5}{y}-{25}\right)}\cdot{\left[{\frac{{{7}}}{{{10}}}}+{y}\right]}={10}{\left({5}{y}-{25}\right)}{\left({2}{y}-{38}\right)}$$
$$\displaystyle{7}{\left({5}{y}-{25}\right)}+{10}{y}{\left({5}{y}-{25}\right)}={10}{\left({5}{y}-{25}\right)}{\left({2}{y}-{38}\right)}$$
Hence the fractions are cleared from the equation.
Therefore the blank is to be filled with $$\displaystyle{10}{\left({5}{y}-{25}\right)}$$.