Basic Math Examples

$\frac{9 h}{7 h - 21} + \frac{8 h}{21 h - 63}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Factor $7$ out of $7 h - 21$ .

Tap for more steps...

Step 1.1.1

Factor $7$ out of $7 h$ .

$\frac{9 h}{7 (h) - 21} + \frac{8 h}{21 h - 63}$

Step 1.1.2

Factor $7$ out of $- 21$ .

$\frac{9 h}{7 h + 7 \cdot - 3} + \frac{8 h}{21 h - 63}$

Step 1.1.3

Factor $7$ out of $7 h + 7 \cdot - 3$ .

$\frac{9 h}{7 (h - 3)} + \frac{8 h}{21 h - 63}$

Step 1.2

Factor $21$ out of $21 h - 63$ .

Tap for more steps...

Step 1.2.1

Factor $21$ out of $21 h$ .

$\frac{9 h}{7 (h - 3)} + \frac{8 h}{21 (h) - 63}$

Step 1.2.2

Factor $21$ out of $- 63$ .

$\frac{9 h}{7 (h - 3)} + \frac{8 h}{21 h + 21 \cdot - 3}$

Step 1.2.3

Factor $21$ out of $21 h + 21 \cdot - 3$ .

$\frac{9 h}{7 (h - 3)} + \frac{8 h}{21 (h - 3)}$

Step 2

To write $\frac{9 h}{7 (h - 3)}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 h}{7 (h - 3)} \cdot \frac{3}{3} + \frac{8 h}{21 (h - 3)}$

Step 3

Write each expression with a common denominator of $21 (h - 3)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{9 h}{7 (h - 3)}$ by $\frac{3}{3}$ .

$\frac{9 h \cdot 3}{7 (h - 3) \cdot 3} + \frac{8 h}{21 (h - 3)}$

Step 3.2

Multiply $3$ by $7$ .

$\frac{9 h \cdot 3}{21 (h - 3)} + \frac{8 h}{21 (h - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 h \cdot 3 + 8 h}{21 (h - 3)}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Factor $h$ out of $9 h \cdot 3 + 8 h$ .

Tap for more steps...

Step 5.1.1

Factor $h$ out of $9 h \cdot 3$ .

$\frac{h (9 \cdot 3) + 8 h}{21 (h - 3)}$

Step 5.1.2

Factor $h$ out of $8 h$ .

$\frac{h (9 \cdot 3) + h \cdot 8}{21 (h - 3)}$

Step 5.1.3

Factor $h$ out of $h (9 \cdot 3) + h \cdot 8$ .

$\frac{h (9 \cdot 3 + 8)}{21 (h - 3)}$

Step 5.2

Multiply $9$ by $3$ .

$\frac{h (27 + 8)}{21 (h - 3)}$

Step 5.3

Add $27$ and $8$ .

$\frac{h \cdot 35}{21 (h - 3)}$

Step 6

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 6.1

Cancel the common factor of $35$ and $21$ .

Tap for more steps...

Step 6.1.1

Factor $7$ out of $h \cdot 35$ .

$\frac{7 (h \cdot 5)}{21 (h - 3)}$

Step 6.1.2

Cancel the common factors.

Tap for more steps...

Step 6.1.2.1

Factor $7$ out of $21 (h - 3)$ .

$\frac{7 (h \cdot 5)}{7 (3 (h - 3))}$

Step 6.1.2.2

Cancel the common factor.

$\frac{7 (h \cdot 5)}{7 (3 (h - 3))}$

Step 6.1.2.3

Rewrite the expression.

$\frac{h \cdot 5}{3 (h - 3)}$

Step 6.2

Move $5$ to the left of $h$ .

$\frac{5 h}{3 (h - 3)}$