Algebra Examples

$6 - \frac{x + 5}{(7 x - 5) (x + 4)}$

Step 1

To write $6$ as a fraction with a common denominator, multiply by $\frac{(7 x - 5) (x + 4)}{(7 x - 5) (x + 4)}$ .

$6 \cdot \frac{(7 x - 5) (x + 4)}{(7 x - 5) (x + 4)} - \frac{x + 5}{(7 x - 5) (x + 4)}$

Step 2

Simplify terms.

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Step 2.1

Combine $6$ and $\frac{(7 x - 5) (x + 4)}{(7 x - 5) (x + 4)}$ .

$\frac{6 ((7 x - 5) (x + 4))}{(7 x - 5) (x + 4)} - \frac{x + 5}{(7 x - 5) (x + 4)}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{6 ((7 x - 5) (x + 4)) - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{(6 (7 x) + 6 \cdot - 5) (x + 4) - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.2

Multiply $7$ by $6$ .

$\frac{(42 x + 6 \cdot - 5) (x + 4) - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.3

Multiply $6$ by $- 5$ .

$\frac{(42 x - 30) (x + 4) - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.4

Expand $(42 x - 30) (x + 4)$ using the FOIL Method.

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Step 3.4.1

Apply the distributive property.

$\frac{42 x (x + 4) - 30 (x + 4) - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.4.2

Apply the distributive property.

$\frac{42 x \cdot x + 42 x \cdot 4 - 30 (x + 4) - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.4.3

Apply the distributive property.

$\frac{42 x \cdot x + 42 x \cdot 4 - 30 x - 30 \cdot 4 - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.5

Simplify and combine like terms.

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Step 3.5.1

Simplify each term.

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Step 3.5.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 3.5.1.1.1

Move $x$ .

$\frac{42 (x \cdot x) + 42 x \cdot 4 - 30 x - 30 \cdot 4 - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.5.1.1.2

Multiply $x$ by $x$ .

$\frac{42 x^{2} + 42 x \cdot 4 - 30 x - 30 \cdot 4 - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.5.1.2

Multiply $4$ by $42$ .

$\frac{42 x^{2} + 168 x - 30 x - 30 \cdot 4 - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.5.1.3

Multiply $- 30$ by $4$ .

$\frac{42 x^{2} + 168 x - 30 x - 120 - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.5.2

Subtract $30 x$ from $168 x$ .

$\frac{42 x^{2} + 138 x - 120 - (x + 5)}{(7 x - 5) (x + 4)}$

Step 3.6

Apply the distributive property.

$\frac{42 x^{2} + 138 x - 120 - x - 1 \cdot 5}{(7 x - 5) (x + 4)}$

Step 3.7

Multiply $- 1$ by $5$ .

$\frac{42 x^{2} + 138 x - 120 - x - 5}{(7 x - 5) (x + 4)}$

Step 3.8

Subtract $x$ from $138 x$ .

$\frac{42 x^{2} + 137 x - 120 - 5}{(7 x - 5) (x + 4)}$

Step 3.9

Subtract $5$ from $- 120$ .

$\frac{42 x^{2} + 137 x - 125}{(7 x - 5) (x + 4)}$