Simplify (t^2s)/(rs)+(rs^2)/(rt)

$\frac{t^{2} s}{r s} + \frac{r s^{2}}{r t}$

Step 1

Simplify each term.

Cancel the common factor of $s$ .

Cancel the common factor.

$\frac{t^{2} s}{r s} + \frac{r s^{2}}{r t}$

Rewrite the expression.

$\frac{t^{2}}{r} + \frac{r s^{2}}{r t}$

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{t^{2}}{r} + \frac{r s^{2}}{r t}$

Rewrite the expression.

$\frac{t^{2}}{r} + \frac{s^{2}}{t}$

Step 2

To write $\frac{t^{2}}{r}$ as a fraction with a common denominator, multiply by $\frac{t}{t}$ .

$\frac{t^{2}}{r} \cdot \frac{t}{t} + \frac{s^{2}}{t}$

Step 3

To write $\frac{s^{2}}{t}$ as a fraction with a common denominator, multiply by $\frac{r}{r}$ .

$\frac{t^{2}}{r} \cdot \frac{t}{t} + \frac{s^{2}}{t} \cdot \frac{r}{r}$

Step 4

Write each expression with a common denominator of $r t$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{t^{2}}{r}$ by $\frac{t}{t}$ .

$\frac{t^{2} t}{r t} + \frac{s^{2}}{t} \cdot \frac{r}{r}$

Multiply $\frac{s^{2}}{t}$ by $\frac{r}{r}$ .

$\frac{t^{2} t}{r t} + \frac{s^{2} r}{t r}$

Reorder the factors of $t r$ .

$\frac{t^{2} t}{r t} + \frac{s^{2} r}{r t}$

Step 5

Combine the numerators over the common denominator.

$\frac{t^{2} t + s^{2} r}{r t}$

Step 6

Multiply $t^{2}$ by $t$ by adding the exponents.

Multiply $t^{2}$ by $t$ .

Raise $t$ to the power of $1$ .

$\frac{t^{2} t^{1} + s^{2} r}{r t}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{t^{2 + 1} + s^{2} r}{r t}$

Add $2$ and $1$ .

$\frac{t^{3} + s^{2} r}{r t}$