Basic Math Examples

$\frac{5}{h + 5} - \frac{4 h - 5}{h (h + 5)}$

Step 1

To write $\frac{5}{h + 5}$ as a fraction with a common denominator, multiply by $\frac{h}{h}$ .

$\frac{5}{h + 5} \cdot \frac{h}{h} - \frac{4 h - 5}{h (h + 5)}$

Step 2

Write each expression with a common denominator of $(h + 5) h$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{5}{h + 5}$ by $\frac{h}{h}$ .

$\frac{5 h}{(h + 5) h} - \frac{4 h - 5}{h (h + 5)}$

Step 2.2

Reorder the factors of $(h + 5) h$ .

$\frac{5 h}{h (h + 5)} - \frac{4 h - 5}{h (h + 5)}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 h - (4 h - 5)}{h (h + 5)}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{5 h - (4 h) - - 5}{h (h + 5)}$

Step 4.2

Multiply $4$ by $- 1$ .

$\frac{5 h - 4 h - - 5}{h (h + 5)}$

Step 4.3

Multiply $- 1$ by $- 5$ .

$\frac{5 h - 4 h + 5}{h (h + 5)}$

Step 4.4

Subtract $4 h$ from $5 h$ .

$\frac{h + 5}{h (h + 5)}$

Step 5

Cancel the common factor of $h + 5$ .

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Step 5.1

Cancel the common factor.

$\frac{h + 5}{h (h + 5)}$

Step 5.2

Rewrite the expression.

$\frac{1}{h}$