Basic Math Examples

$(\frac{r t s}{r s}) - (\frac{1}{s}) + \frac{s}{r (r - s)}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $r$ .

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Step 1.1.1

Cancel the common factor.

$\frac{r t s}{r s} - (\frac{1}{s}) + \frac{s}{r (r - s)}$

Step 1.1.2

Rewrite the expression.

$\frac{t s}{s} - (\frac{1}{s}) + \frac{s}{r (r - s)}$

Step 1.2

Cancel the common factor of $s$ .

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Step 1.2.1

Cancel the common factor.

$\frac{t s}{s} - (\frac{1}{s}) + \frac{s}{r (r - s)}$

Step 1.2.2

Divide $t$ by $1$ .

$t - (\frac{1}{s}) + \frac{s}{r (r - s)}$

$t - \frac{1}{s} + \frac{s}{r (r - s)}$

Step 2

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

$\frac{t s}{s} - \frac{1}{s} + \frac{s}{r (r - s)}$

Step 3

Combine the numerators over the common denominator.

$\frac{t s - 1}{s} + \frac{s}{r (r - s)}$

Step 4

To write $\frac{t s - 1}{s}$ as a fraction with a common denominator, multiply by $\frac{r (r - s)}{r (r - s)}$ .

$\frac{t s - 1}{s} \cdot \frac{r (r - s)}{r (r - s)} + \frac{s}{r (r - s)}$

Step 5

To write $\frac{s}{r (r - s)}$ as a fraction with a common denominator, multiply by $\frac{s}{s}$ .

$\frac{t s - 1}{s} \cdot \frac{r (r - s)}{r (r - s)} + \frac{s}{r (r - s)} \cdot \frac{s}{s}$

Step 6

Write each expression with a common denominator of $s r (r - s)$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{t s - 1}{s}$ by $\frac{r (r - s)}{r (r - s)}$ .

$\frac{(t s - 1) (r (r - s))}{s (r (r - s))} + \frac{s}{r (r - s)} \cdot \frac{s}{s}$

Step 6.2

Multiply $\frac{s}{r (r - s)}$ by $\frac{s}{s}$ .

$\frac{(t s - 1) (r (r - s))}{s (r (r - s))} + \frac{s \cdot s}{r (r - s) s}$

Step 6.3

Reorder the factors of $s (r (r - s))$ .

$\frac{(t s - 1) (r (r - s))}{r s (r - s)} + \frac{s \cdot s}{r (r - s) s}$

Step 6.4

Reorder the factors of $r (r - s) s$ .

$\frac{(t s - 1) (r (r - s))}{r s (r - s)} + \frac{s \cdot s}{r s (r - s)}$

Step 7

Combine the numerators over the common denominator.

$\frac{(t s - 1) (r (r - s)) + s \cdot s}{r s (r - s)}$

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{(t s r - 1 r) (r - s) + s \cdot s}{r s (r - s)}$

Step 8.2

Rewrite $- 1 r$ as $- r$ .

$\frac{(t s r - r) (r - s) + s \cdot s}{r s (r - s)}$

Step 8.3

Expand $(t s r - r) (r - s)$ using the FOIL Method.

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Step 8.3.1

Apply the distributive property.

$\frac{t s r (r - s) - r (r - s) + s \cdot s}{r s (r - s)}$

Step 8.3.2

Apply the distributive property.

$\frac{t s r \cdot r + t s r (- s) - r (r - s) + s \cdot s}{r s (r - s)}$

Step 8.3.3

Apply the distributive property.

$\frac{t s r \cdot r + t s r (- s) - r \cdot r - r (- s) + s \cdot s}{r s (r - s)}$

Step 8.4

Simplify each term.

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Step 8.4.1

Multiply $r$ by $r$ by adding the exponents.

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Step 8.4.1.1

Move $r$ .

$\frac{t s (r \cdot r) + t s r (- s) - r \cdot r - r (- s) + s \cdot s}{r s (r - s)}$

Step 8.4.1.2

Multiply $r$ by $r$ .

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

Step 8.4.2

Rewrite using the commutative property of multiplication.

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

Step 8.4.3

Multiply $s$ by $s$ by adding the exponents.

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Step 8.4.3.1

Move $s$ .

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

Step 8.4.3.2

Multiply $s$ by $s$ .

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

Step 8.4.4

Multiply $r$ by $r$ by adding the exponents.

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Step 8.4.4.1

Move $r$ .

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

Step 8.4.4.2

Multiply $r$ by $r$ .

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

Step 8.4.5

Rewrite using the commutative property of multiplication.

$\frac{t s r^{2} - t s^{2} r - r^{2} - 1 \cdot - 1 r s + s \cdot s}{r s (r - s)}$

Step 8.4.6

Multiply $- 1$ by $- 1$ .

$\frac{t s r^{2} - t s^{2} r - r^{2} + 1 r s + s \cdot s}{r s (r - s)}$

Step 8.4.7

Multiply $r$ by $1$ .

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

Step 8.5

Multiply $s$ by $s$ .

$\frac{t s r^{2} - t s^{2} r - r^{2} + r s + s^{2}}{r s (r - s)}$