Solve 5/frac{29{7}}-3/x-1

$$\frac { 5 } { \frac { 29 } { 7 } } - \frac { 3 } { x - 1 }$$

Evaluate

$$\frac{35x-122}{29\left(x-1\right)}$$

Short Solution Steps

Divide 5 by \frac{29}{7} by multiplying 5 by the reciprocal of \frac{29}{7}.

$$5\times \frac{7}{29}-\frac{3}{x-1}$$

Express 5\times \frac{7}{29} as a single fraction.

$$\frac{5\times 7}{29}-\frac{3}{x-1}$$

Multiply 5 and 7 to get 35.

$$\frac{35}{29}-\frac{3}{x-1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 29 and x-1 is 29\left(x-1\right). Multiply \frac{35}{29} times \frac{x-1}{x-1}. Multiply \frac{3}{x-1} times \frac{29}{29}.

$$\frac{35\left(x-1\right)}{29\left(x-1\right)}-\frac{3\times 29}{29\left(x-1\right)}$$

Since \frac{35\left(x-1\right)}{29\left(x-1\right)} and \frac{3\times 29}{29\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35\left(x-1\right)-3\times 29}{29\left(x-1\right)}$$

Do the multiplications in 35\left(x-1\right)-3\times 29.

$$\frac{35x-35-87}{29\left(x-1\right)}$$

Combine like terms in 35x-35-87.

$$\frac{35x-122}{29\left(x-1\right)}$$

Expand 29\left(x-1\right).

$$\frac{35x-122}{29x-29}$$

Factor

$$\frac{35x-122}{29\left(x-1\right)}$$