Subtract x/(7x-9)-(x+3)/(8x)

$\frac{x}{7 x - 9} - \frac{x + 3}{8 x}$

To write $\frac{x}{7 x - 9}$ as a fraction with a common denominator, multiply by $\frac{8 x}{8 x}$ .

$\frac{x}{7 x - 9} \cdot \frac{8 x}{8 x} - \frac{x + 3}{8 x}$

To write $- \frac{x + 3}{8 x}$ as a fraction with a common denominator, multiply by $\frac{7 x - 9}{7 x - 9}$ .

$\frac{x}{7 x - 9} \cdot \frac{8 x}{8 x} - \frac{x + 3}{8 x} \cdot \frac{7 x - 9}{7 x - 9}$

Write each expression with a common denominator of $(7 x - 9) \cdot 8 x$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{x}{7 x - 9}$ and $\frac{8 x}{8 x}$ .

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

Multiply $\frac{x + 3}{8 x}$ and $\frac{7 x - 9}{7 x - 9}$ .

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

Reorder the factors of $(7 x - 9) (8 x)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Rewrite using the commutative property of multiplication.

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

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

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Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{8 x^{2} - (x + 3) (7 x - 9)}{8 x (7 x - 9)}$

Apply the distributive property.

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

Multiply $- 1$ by $3$ .

$\frac{8 x^{2} + (- x - 3) (7 x - 9)}{8 x (7 x - 9)}$

Expand $(- x - 3) (7 x - 9)$ using the FOIL Method.

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Apply the distributive property.

$\frac{8 x^{2} - x (7 x - 9) - 3 (7 x - 9)}{8 x (7 x - 9)}$

Apply the distributive property.

$\frac{8 x^{2} - x (7 x) - x \cdot - 9 - 3 (7 x - 9)}{8 x (7 x - 9)}$

Apply the distributive property.

$\frac{8 x^{2} - x (7 x) - x \cdot - 9 - 3 (7 x) - 3 \cdot - 9}{8 x (7 x - 9)}$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$\frac{8 x^{2} - 1 \cdot 7 x^{2} - x \cdot - 9 - 3 (7 x) - 3 \cdot - 9}{8 x (7 x - 9)}$

Multiply $- 1$ by $7$ .

$\frac{8 x^{2} - 7 x^{2} - x \cdot - 9 - 3 (7 x) - 3 \cdot - 9}{8 x (7 x - 9)}$

Multiply $- 9$ by $- 1$ .

$\frac{8 x^{2} - 7 x^{2} + 9 x - 3 (7 x) - 3 \cdot - 9}{8 x (7 x - 9)}$

Multiply $7$ by $- 3$ .

$\frac{8 x^{2} - 7 x^{2} + 9 x - 21 x - 3 \cdot - 9}{8 x (7 x - 9)}$

Multiply $- 3$ by $- 9$ .

$\frac{8 x^{2} - 7 x^{2} + 9 x - 21 x + 27}{8 x (7 x - 9)}$

Subtract $21 x$ from $9 x$ .

$\frac{8 x^{2} - 7 x^{2} - 12 x + 27}{8 x (7 x - 9)}$

Subtract $7 x^{2}$ from $8 x^{2}$ .

$\frac{x^{2} - 12 x + 27}{8 x (7 x - 9)}$

Factor $x^{2} - 12 x + 27$ using the AC method.

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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 $27$ and whose sum is $- 12$ .

$- 9, - 3$

Write the factored form using these integers.

$\frac{(x - 9) (x - 3)}{8 x (7 x - 9)}$

Subtract x/(7x-9)-(x+3)/(8x)

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