Solve r/3-3/r/frac{r{4}-4/r}

$$\frac { \frac { r } { 3 } - \frac { 3 } { r } } { \frac { r } { 4 } - \frac { 4 } { r } }$$

Evaluate

$$\frac{4\left(r^{2}-9\right)}{3\left(r^{2}-16\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and r is 3r. Multiply \frac{r}{3} times \frac{r}{r}. Multiply \frac{3}{r} times \frac{3}{3}.

$$\frac{\frac{rr}{3r}-\frac{3\times 3}{3r}}{\frac{r}{4}-\frac{4}{r}}$$

Since \frac{rr}{3r} and \frac{3\times 3}{3r} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{rr-3\times 3}{3r}}{\frac{r}{4}-\frac{4}{r}}$$

Do the multiplications in rr-3\times 3.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{r}{4}-\frac{4}{r}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and r is 4r. Multiply \frac{r}{4} times \frac{r}{r}. Multiply \frac{4}{r} times \frac{4}{4}.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{rr}{4r}-\frac{4\times 4}{4r}}$$

Since \frac{rr}{4r} and \frac{4\times 4}{4r} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{rr-4\times 4}{4r}}$$

Do the multiplications in rr-4\times 4.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{r^{2}-16}{4r}}$$

Divide \frac{r^{2}-9}{3r} by \frac{r^{2}-16}{4r} by multiplying \frac{r^{2}-9}{3r} by the reciprocal of \frac{r^{2}-16}{4r}.

$$\frac{\left(r^{2}-9\right)\times 4r}{3r\left(r^{2}-16\right)}$$

Cancel out r in both numerator and denominator.

$$\frac{4\left(r^{2}-9\right)}{3\left(r^{2}-16\right)}$$

Use the distributive property to multiply 4 by r^{2}-9.

$$\frac{4r^{2}-36}{3\left(r^{2}-16\right)}$$

Use the distributive property to multiply 3 by r^{2}-16.

$$\frac{4r^{2}-36}{3r^{2}-48}$$

Expand

$$\frac{4\left(r^{2}-9\right)}{3\left(r^{2}-16\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and r is 3r. Multiply \frac{r}{3} times \frac{r}{r}. Multiply \frac{3}{r} times \frac{3}{3}.

$$\frac{\frac{rr}{3r}-\frac{3\times 3}{3r}}{\frac{r}{4}-\frac{4}{r}}$$

Since \frac{rr}{3r} and \frac{3\times 3}{3r} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{rr-3\times 3}{3r}}{\frac{r}{4}-\frac{4}{r}}$$

Do the multiplications in rr-3\times 3.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{r}{4}-\frac{4}{r}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and r is 4r. Multiply \frac{r}{4} times \frac{r}{r}. Multiply \frac{4}{r} times \frac{4}{4}.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{rr}{4r}-\frac{4\times 4}{4r}}$$

Since \frac{rr}{4r} and \frac{4\times 4}{4r} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{rr-4\times 4}{4r}}$$

Do the multiplications in rr-4\times 4.

$$\frac{\frac{r^{2}-9}{3r}}{\frac{r^{2}-16}{4r}}$$

Divide \frac{r^{2}-9}{3r} by \frac{r^{2}-16}{4r} by multiplying \frac{r^{2}-9}{3r} by the reciprocal of \frac{r^{2}-16}{4r}.

$$\frac{\left(r^{2}-9\right)\times 4r}{3r\left(r^{2}-16\right)}$$

Cancel out r in both numerator and denominator.

$$\frac{4\left(r^{2}-9\right)}{3\left(r^{2}-16\right)}$$

Use the distributive property to multiply 4 by r^{2}-9.

$$\frac{4r^{2}-36}{3\left(r^{2}-16\right)}$$

Use the distributive property to multiply 3 by r^{2}-16.

$$\frac{4r^{2}-36}{3r^{2}-48}$$