Solve q/r+1/frac{r{q}-1}

$$\frac { \frac { q } { r } + 1 } { \frac { r } { q } - 1 }$$

Evaluate

$$\frac{q\left(q+r\right)}{r\left(r-q\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{r}{r}.

$$\frac{\frac{q}{r}+\frac{r}{r}}{\frac{r}{q}-1}$$

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

$$\frac{\frac{q+r}{r}}{\frac{r}{q}-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{q}{q}.

$$\frac{\frac{q+r}{r}}{\frac{r}{q}-\frac{q}{q}}$$

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

$$\frac{\frac{q+r}{r}}{\frac{r-q}{q}}$$

Divide \frac{q+r}{r} by \frac{r-q}{q} by multiplying \frac{q+r}{r} by the reciprocal of \frac{r-q}{q}.

$$\frac{\left(q+r\right)q}{r\left(r-q\right)}$$

Use the distributive property to multiply q+r by q.

$$\frac{q^{2}+rq}{r\left(r-q\right)}$$

Use the distributive property to multiply r by r-q.

$$\frac{q^{2}+rq}{r^{2}-rq}$$

Expand

$$\frac{q^{2}+qr}{r\left(r-q\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{r}{r}.

$$\frac{\frac{q}{r}+\frac{r}{r}}{\frac{r}{q}-1}$$

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

$$\frac{\frac{q+r}{r}}{\frac{r}{q}-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{q}{q}.

$$\frac{\frac{q+r}{r}}{\frac{r}{q}-\frac{q}{q}}$$

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

$$\frac{\frac{q+r}{r}}{\frac{r-q}{q}}$$

Divide \frac{q+r}{r} by \frac{r-q}{q} by multiplying \frac{q+r}{r} by the reciprocal of \frac{r-q}{q}.

$$\frac{\left(q+r\right)q}{r\left(r-q\right)}$$

Use the distributive property to multiply q+r by q.

$$\frac{q^{2}+rq}{r\left(r-q\right)}$$

Use the distributive property to multiply r by r-q.

$$\frac{q^{2}+rq}{r^{2}-rq}$$