Algebra Examples

$\frac{35 x^{2} + 50 x}{5 x} \div \frac{7 x^{2} + 66 x + 80}{3 x - 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{35 x^{2} + 50 x}{5 x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 2

Factor $5 x$ out of $35 x^{2} + 50 x$ .

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Step 2.1

Factor $5 x$ out of $35 x^{2}$ .

$\frac{5 x (7 x) + 50 x}{5 x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 2.2

Factor $5 x$ out of $50 x$ .

$\frac{5 x (7 x) + 5 x (10)}{5 x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 2.3

Factor $5 x$ out of $5 x (7 x) + 5 x (10)$ .

$\frac{5 x (7 x + 10)}{5 x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 x (7 x + 10)}{5 x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 3.2

Rewrite the expression.

$\frac{x (7 x + 10)}{x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\frac{x (7 x + 10)}{x} \cdot \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 4.2

Divide $7 x + 10$ by $1$ .

$(7 x + 10) \frac{3 x - 3}{7 x^{2} + 66 x + 80}$

Step 5

Factor $3$ out of $3 x - 3$ .

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Step 5.1

Factor $3$ out of $3 x$ .

$(7 x + 10) \frac{3 (x) - 3}{7 x^{2} + 66 x + 80}$

Step 5.2

Factor $3$ out of $- 3$ .

$(7 x + 10) \frac{3 (x) + 3 (- 1)}{7 x^{2} + 66 x + 80}$

Step 5.3

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$(7 x + 10) \frac{3 (x - 1)}{7 x^{2} + 66 x + 80}$

Step 6

Factor by grouping.

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Step 6.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 7 \cdot 80 = 560$ and whose sum is $b = 66$ .

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Step 6.1.1

Factor $66$ out of $66 x$ .

$(7 x + 10) \frac{3 (x - 1)}{7 x^{2} + 66 (x) + 80}$

Step 6.1.2

Rewrite $66$ as $10$ plus $56$

$(7 x + 10) \frac{3 (x - 1)}{7 x^{2} + (10 + 56) x + 80}$

Step 6.1.3

Apply the distributive property.

$(7 x + 10) \frac{3 (x - 1)}{7 x^{2} + 10 x + 56 x + 80}$

Step 6.2

Factor out the greatest common factor from each group.

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Step 6.2.1

Group the first two terms and the last two terms.

$(7 x + 10) \frac{3 (x - 1)}{(7 x^{2} + 10 x) + 56 x + 80}$

Step 6.2.2

Factor out the greatest common factor (GCF) from each group.

$(7 x + 10) \frac{3 (x - 1)}{x (7 x + 10) + 8 (7 x + 10)}$

Step 6.3

Factor the polynomial by factoring out the greatest common factor, $7 x + 10$ .

$(7 x + 10) \frac{3 (x - 1)}{(7 x + 10) (x + 8)}$

Step 7

Cancel the common factor of $7 x + 10$ .

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Step 7.1

Cancel the common factor.

$(7 x + 10) \frac{3 (x - 1)}{(7 x + 10) (x + 8)}$

Step 7.2

Rewrite the expression.

$\frac{3 (x - 1)}{x + 8}$