Basic Math Examples

$\frac{y^{2} + 4 y + 3}{y^{2} - 8 y + 7} \div \frac{y^{2} - 7 y - 8}{y^{2} - 2 y - 35} \div \frac{y^{2} + 8 y + 15}{y^{2} - 9 y + 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y^{2} + 4 y + 3}{y^{2} - 8 y + 7} \div \frac{y^{2} - 7 y - 8}{y^{2} - 2 y - 35} \cdot \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{y^{2} + 4 y + 3}{y^{2} - 8 y + 7} \cdot \frac{y^{2} - 2 y - 35}{y^{2} - 7 y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 3

Factor $y^{2} + 4 y + 3$ using the AC method.

Tap for more steps...

Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $4$ .

$1, 3$

Step 3.2

Write the factored form using these integers.

$\frac{(y + 1) (y + 3)}{y^{2} - 8 y + 7} \cdot \frac{y^{2} - 2 y - 35}{y^{2} - 7 y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 4

Factor $y^{2} - 8 y + 7$ using the AC method.

Tap for more steps...

Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $7$ and whose sum is $- 8$ .

$- 7, - 1$

Step 4.2

Write the factored form using these integers.

$\frac{(y + 1) (y + 3)}{(y - 7) (y - 1)} \cdot \frac{y^{2} - 2 y - 35}{y^{2} - 7 y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 5

Factor $y^{2} - 2 y - 35$ using the AC method.

Tap for more steps...

Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 35$ and whose sum is $- 2$ .

$- 7, 5$

Step 5.2

Write the factored form using these integers.

$\frac{(y + 1) (y + 3)}{(y - 7) (y - 1)} \cdot \frac{(y - 7) (y + 5)}{y^{2} - 7 y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 6

Factor $y^{2} - 7 y - 8$ using the AC method.

Tap for more steps...

Step 6.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $- 7$ .

$- 8, 1$

Step 6.2

Write the factored form using these integers.

$\frac{(y + 1) (y + 3)}{(y - 7) (y - 1)} \cdot \frac{(y - 7) (y + 5)}{(y - 8) (y + 1)} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Cancel the common factor of $y + 1$ .

Tap for more steps...

Step 7.1.1

Factor $y + 1$ out of $(y - 8) (y + 1)$ .

$\frac{(y + 1) (y + 3)}{(y - 7) (y - 1)} \cdot \frac{(y - 7) (y + 5)}{(y + 1) (y - 8)} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 7.1.2

Cancel the common factor.

$\frac{(y + 1) (y + 3)}{(y - 7) (y - 1)} \cdot \frac{(y - 7) (y + 5)}{(y + 1) (y - 8)} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 7.1.3

Rewrite the expression.

$\frac{y + 3}{(y - 7) (y - 1)} \cdot \frac{(y - 7) (y + 5)}{y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 7.2

Cancel the common factor of $y - 7$ .

Tap for more steps...

Step 7.2.1

Cancel the common factor.

$\frac{y + 3}{(y - 7) (y - 1)} \cdot \frac{(y - 7) (y + 5)}{y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 7.2.2

Rewrite the expression.

$\frac{y + 3}{y - 1} \cdot \frac{y + 5}{y - 8} \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 7.3

Multiply $\frac{y + 3}{y - 1}$ by $\frac{y + 5}{y - 8}$ .

$\frac{(y + 3) (y + 5)}{(y - 1) (y - 8)} \cdot \frac{y^{2} - 9 y + 8}{y^{2} + 8 y + 15}$

Step 8

Factor $y^{2} - 9 y + 8$ using the AC method.

Tap for more steps...

Step 8.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $- 9$ .

$- 8, - 1$

Step 8.2

Write the factored form using these integers.

$\frac{(y + 3) (y + 5)}{(y - 1) (y - 8)} \cdot \frac{(y - 8) (y - 1)}{y^{2} + 8 y + 15}$

Step 9

Factor $y^{2} + 8 y + 15$ using the AC method.

Tap for more steps...

Step 9.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $15$ and whose sum is $8$ .

$3, 5$

Step 9.2

Write the factored form using these integers.

$\frac{(y + 3) (y + 5)}{(y - 1) (y - 8)} \cdot \frac{(y - 8) (y - 1)}{(y + 3) (y + 5)}$

Step 10

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 10.1

Cancel the common factor of $(y + 3) (y + 5)$ .

Tap for more steps...

Step 10.1.1

Cancel the common factor.

$\frac{(y + 3) (y + 5)}{(y - 1) (y - 8)} \cdot \frac{(y - 8) (y - 1)}{(y + 3) (y + 5)}$

Step 10.1.2

Rewrite the expression.

$\frac{1}{(y - 1) (y - 8)} ((y - 8) (y - 1))$

Step 10.2

Cancel the common factor of $(y - 8) (y - 1)$ .

Tap for more steps...

Step 10.2.1

Factor $(y - 8) (y - 1)$ out of $(y - 1) (y - 8)$ .

$\frac{1}{(y - 8) (y - 1) (1)} ((y - 8) (y - 1))$

Step 10.2.2

Cancel the common factor.

$\frac{1}{(y - 8) (y - 1) \cdot 1} ((y - 8) (y - 1))$

Step 10.2.3

Rewrite the expression.

$1$