Solve 4/1-frac{-1{7}}=3/1+frac{-1{7}}

$$\frac{ 4 }{ 1- \frac{ -1 }{ 7 } } = \frac{ 3 }{ 1+ \frac{ -1 }{ 7 } }$$

Verify

Solution Steps

Fraction \frac{-1}{7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$\frac{4}{1-\left(-\frac{1}{7}\right)}=\frac{3}{1+\frac{-1}{7}}$$

The opposite of -\frac{1}{7} is \frac{1}{7}.

$$\frac{4}{1+\frac{1}{7}}=\frac{3}{1+\frac{-1}{7}}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{4}{\frac{7}{7}+\frac{1}{7}}=\frac{3}{1+\frac{-1}{7}}$$

Since \frac{7}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{4}{\frac{7+1}{7}}=\frac{3}{1+\frac{-1}{7}}$$

Add 7 and 1 to get 8.

$$\frac{4}{\frac{8}{7}}=\frac{3}{1+\frac{-1}{7}}$$

Divide 4 by \frac{8}{7} by multiplying 4 by the reciprocal of \frac{8}{7}.

$$4\times \frac{7}{8}=\frac{3}{1+\frac{-1}{7}}$$

Express 4\times \frac{7}{8} as a single fraction.

$$\frac{4\times 7}{8}=\frac{3}{1+\frac{-1}{7}}$$

Multiply 4 and 7 to get 28.

$$\frac{28}{8}=\frac{3}{1+\frac{-1}{7}}$$

Reduce the fraction \frac{28}{8} to lowest terms by extracting and canceling out 4.

$$\frac{7}{2}=\frac{3}{1+\frac{-1}{7}}$$

Fraction \frac{-1}{7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$\frac{7}{2}=\frac{3}{1-\frac{1}{7}}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{7}{2}=\frac{3}{\frac{7}{7}-\frac{1}{7}}$$

Since \frac{7}{7} and \frac{1}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}=\frac{3}{\frac{7-1}{7}}$$

Subtract 1 from 7 to get 6.

$$\frac{7}{2}=\frac{3}{\frac{6}{7}}$$

Divide 3 by \frac{6}{7} by multiplying 3 by the reciprocal of \frac{6}{7}.

$$\frac{7}{2}=3\times \frac{7}{6}$$

Express 3\times \frac{7}{6} as a single fraction.

$$\frac{7}{2}=\frac{3\times 7}{6}$$

Multiply 3 and 7 to get 21.

$$\frac{7}{2}=\frac{21}{6}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}=\frac{7}{2}$$

Compare \frac{7}{2} and \frac{7}{2}.

$$\text{true}$$