Subtract (-5x)/(8x+7)-(6x^3)/(3x+1)

$\frac{- 5 x}{8 x + 7} - \frac{6 x^{3}}{3 x + 1}$

Move the negative in front of the fraction.

$- \frac{5 x}{8 x + 7} - \frac{6 x^{3}}{3 x + 1}$

To write $- \frac{5 x}{8 x + 7}$ as a fraction with a common denominator, multiply by $\frac{3 x + 1}{3 x + 1}$ .

$- \frac{5 x}{8 x + 7} \cdot \frac{3 x + 1}{3 x + 1} - \frac{6 x^{3}}{3 x + 1}$

To write $- \frac{6 x^{3}}{3 x + 1}$ as a fraction with a common denominator, multiply by $\frac{8 x + 7}{8 x + 7}$ .

$- \frac{5 x}{8 x + 7} \cdot \frac{3 x + 1}{3 x + 1} - \frac{6 x^{3}}{3 x + 1} \cdot \frac{8 x + 7}{8 x + 7}$

Write each expression with a common denominator of $(8 x + 7) (3 x + 1)$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{5 x}{8 x + 7}$ and $\frac{3 x + 1}{3 x + 1}$ .

$- \frac{5 x (3 x + 1)}{(8 x + 7) (3 x + 1)} - \frac{6 x^{3}}{3 x + 1} \cdot \frac{8 x + 7}{8 x + 7}$

Multiply $\frac{6 x^{3}}{3 x + 1}$ and $\frac{8 x + 7}{8 x + 7}$ .

$- \frac{5 x (3 x + 1)}{(8 x + 7) (3 x + 1)} - \frac{6 x^{3} (8 x + 7)}{(3 x + 1) (8 x + 7)}$

Reorder the factors of $(8 x + 7) (3 x + 1)$ .

$- \frac{5 x (3 x + 1)}{(3 x + 1) (8 x + 7)} - \frac{6 x^{3} (8 x + 7)}{(3 x + 1) (8 x + 7)}$

Combine the numerators over the common denominator.

$\frac{- 5 x (3 x + 1) - 6 x^{3} (8 x + 7)}{(3 x + 1) (8 x + 7)}$

Simplify the numerator.

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Factor $x$ out of $- 5 x (3 x + 1) - 6 x^{3} (8 x + 7)$ .

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Factor $x$ out of $- 5 x (3 x + 1)$ .

$\frac{x (- 5 (3 x + 1)) - 6 x^{3} (8 x + 7)}{(3 x + 1) (8 x + 7)}$

Factor $x$ out of $- 6 x^{3} (8 x + 7)$ .

$\frac{x (- 5 (3 x + 1)) + x (- 6 x^{2} (8 x + 7))}{(3 x + 1) (8 x + 7)}$

Factor $x$ out of $x (- 5 (3 x + 1)) + x (- 6 x^{2} (8 x + 7))$ .

$\frac{x (- 5 (3 x + 1) - 6 x^{2} (8 x + 7))}{(3 x + 1) (8 x + 7)}$

Apply the distributive property.

$\frac{x (- 5 (3 x) - 5 \cdot 1 - 6 x^{2} (8 x + 7))}{(3 x + 1) (8 x + 7)}$

Multiply $3$ by $- 5$ .

$\frac{x (- 15 x - 5 \cdot 1 - 6 x^{2} (8 x + 7))}{(3 x + 1) (8 x + 7)}$

Multiply $- 5$ by $1$ .

$\frac{x (- 15 x - 5 - 6 x^{2} (8 x + 7))}{(3 x + 1) (8 x + 7)}$

Apply the distributive property.

$\frac{x (- 15 x - 5 - 6 x^{2} (8 x) - 6 x^{2} \cdot 7)}{(3 x + 1) (8 x + 7)}$

Rewrite using the commutative property of multiplication.

$\frac{x (- 15 x - 5 - 6 \cdot 8 (x^{2} x) - 6 x^{2} \cdot 7)}{(3 x + 1) (8 x + 7)}$

Multiply $7$ by $- 6$ .

$\frac{x (- 15 x - 5 - 6 \cdot 8 (x^{2} x) - 42 x^{2})}{(3 x + 1) (8 x + 7)}$

Simplify each term.

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Multiply $x^{2}$ by $x$ by adding the exponents.

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Multiply $x^{2}$ by $x$ .

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Raise $x$ to the power of $1$ .

$\frac{x (- 15 x - 5 - 6 \cdot 8 (x^{2} x^{1}) - 42 x^{2})}{(3 x + 1) (8 x + 7)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x (- 15 x - 5 - 6 \cdot 8 x^{2 + 1} - 42 x^{2})}{(3 x + 1) (8 x + 7)}$

Add $2$ and $1$ .

$\frac{x (- 15 x - 5 - 6 \cdot 8 x^{3} - 42 x^{2})}{(3 x + 1) (8 x + 7)}$

Multiply $- 6$ by $8$ .

$\frac{x (- 15 x - 5 - 48 x^{3} - 42 x^{2})}{(3 x + 1) (8 x + 7)}$

Reorder terms.

$\frac{x (- 48 x^{3} - 42 x^{2} - 15 x - 5)}{(3 x + 1) (8 x + 7)}$

Simplify with factoring out.

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Factor $- 1$ out of $- 48 x^{3}$ .

$\frac{x (- (48 x^{3}) - 42 x^{2} - 15 x - 5)}{(3 x + 1) (8 x + 7)}$

Factor $- 1$ out of $- 42 x^{2}$ .

$\frac{x (- (48 x^{3}) - (42 x^{2}) - 15 x - 5)}{(3 x + 1) (8 x + 7)}$

Factor $- 1$ out of $- (48 x^{3}) - (42 x^{2})$ .

$\frac{x (- (48 x^{3} + 42 x^{2}) - 15 x - 5)}{(3 x + 1) (8 x + 7)}$

Factor $- 1$ out of $- 15 x$ .

$\frac{x (- (48 x^{3} + 42 x^{2}) - (15 x) - 5)}{(3 x + 1) (8 x + 7)}$

Factor $- 1$ out of $- (48 x^{3} + 42 x^{2}) - (15 x)$ .

$\frac{x (- (48 x^{3} + 42 x^{2} + 15 x) - 5)}{(3 x + 1) (8 x + 7)}$

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{x (- (48 x^{3} + 42 x^{2} + 15 x) - 1 (5))}{(3 x + 1) (8 x + 7)}$

Factor $- 1$ out of $- (48 x^{3} + 42 x^{2} + 15 x) - 1 (5)$ .

$\frac{x (- (48 x^{3} + 42 x^{2} + 15 x + 5))}{(3 x + 1) (8 x + 7)}$

Simplify the expression.

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Rewrite $- (48 x^{3} + 42 x^{2} + 15 x + 5)$ as $- 1 (48 x^{3} + 42 x^{2} + 15 x + 5)$ .

$\frac{x (- 1 (48 x^{3} + 42 x^{2} + 15 x + 5))}{(3 x + 1) (8 x + 7)}$

Move the negative in front of the fraction.

$- \frac{x (48 x^{3} + 42 x^{2} + 15 x + 5)}{(3 x + 1) (8 x + 7)}$

Subtract (-5x)/(8x+7)-(6x^3)/(3x+1)

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