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 \(\displaystyle{10}{\left({5}{y}-{25}\right)}\).

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 \(\displaystyle{10}{\left({5}{y}-{25}\right)}\).