Simplify 5/(2x)-(3x)/(x+1)

$\frac{5}{2 x} - \frac{3 x}{x + 1}$

Step 1

To write $\frac{5}{2 x}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{5}{2 x} \cdot \frac{x + 1}{x + 1} - \frac{3 x}{x + 1}$

Step 2

To write $- \frac{3 x}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{5}{2 x} \cdot \frac{x + 1}{x + 1} - \frac{3 x}{x + 1} \cdot \frac{2 x}{2 x}$

Step 3

Write each expression with a common denominator of $2 x (x + 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{2 x}$ by $\frac{x + 1}{x + 1}$ .

$\frac{5 (x + 1)}{2 x (x + 1)} - \frac{3 x}{x + 1} \cdot \frac{2 x}{2 x}$

Multiply $\frac{3 x}{x + 1}$ by $\frac{2 x}{2 x}$ .

$\frac{5 (x + 1)}{2 x (x + 1)} - \frac{3 x (2 x)}{(x + 1) (2 x)}$

Reorder the factors of $(x + 1) (2 x)$ .

$\frac{5 (x + 1)}{2 x (x + 1)} - \frac{3 x (2 x)}{2 x (x + 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (x + 1) - 3 x (2 x)}{2 x (x + 1)}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{5 x + 5 \cdot 1 - 3 x (2 x)}{2 x (x + 1)}$

Multiply $5$ by $1$ .

$\frac{5 x + 5 - 3 x (2 x)}{2 x (x + 1)}$

Rewrite using the commutative property of multiplication.

$\frac{5 x + 5 - 3 \cdot 2 x \cdot x}{2 x (x + 1)}$

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

Move $x$ .

$\frac{5 x + 5 - 3 \cdot 2 (x \cdot x)}{2 x (x + 1)}$

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $2$ .

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

Reorder terms.

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

Step 6

Simplify with factoring out.

Factor $- 1$ out of $- 6 x^{2}$ .

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

Factor $- 1$ out of $5 x$ .

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

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

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

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

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

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

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

Simplify the expression.

Rewrite $- (6 x^{2} - 5 x - 5)$ as $- 1 (6 x^{2} - 5 x - 5)$ .

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

Move the negative in front of the fraction.

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

Simplify 5/(2x)-(3x)/(x+1)

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