Simplify (x-4)/(2x)+(2x+3)/(2x-3)

$\frac{x - 4}{2 x} + \frac{2 x + 3}{2 x - 3}$

To write $\frac{x - 4}{2 x}$ as a fraction with a common denominator, multiply by $\frac{2 x - 3}{2 x - 3}$ .

$\frac{x - 4}{2 x} \cdot \frac{2 x - 3}{2 x - 3} + \frac{2 x + 3}{2 x - 3}$

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

$\frac{x - 4}{2 x} \cdot \frac{2 x - 3}{2 x - 3} + \frac{2 x + 3}{2 x - 3} \cdot \frac{2 x}{2 x}$

Write each expression with a common denominator of $2 x (2 x - 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 4}{2 x}$ by $\frac{2 x - 3}{2 x - 3}$ .

$\frac{(x - 4) (2 x - 3)}{2 x (2 x - 3)} + \frac{2 x + 3}{2 x - 3} \cdot \frac{2 x}{2 x}$

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

$\frac{(x - 4) (2 x - 3)}{2 x (2 x - 3)} + \frac{(2 x + 3) (2 x)}{(2 x - 3) (2 x)}$

Reorder the factors of $(2 x - 3) (2 x)$ .

$\frac{(x - 4) (2 x - 3)}{2 x (2 x - 3)} + \frac{(2 x + 3) (2 x)}{2 x (2 x - 3)}$

Combine the numerators over the common denominator.

$\frac{(x - 4) (2 x - 3) + (2 x + 3) (2 x)}{2 x (2 x - 3)}$

Simplify the numerator.

Expand $(x - 4) (2 x - 3)$ using the FOIL Method.

Apply the distributive property.

$\frac{x (2 x - 3) - 4 (2 x - 3) + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Apply the distributive property.

$\frac{x (2 x) + x \cdot - 3 - 4 (2 x - 3) + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Apply the distributive property.

$\frac{x (2 x) + x \cdot - 3 - 4 (2 x) - 4 \cdot - 3 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$\frac{2 x \cdot x + x \cdot - 3 - 4 (2 x) - 4 \cdot - 3 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

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

Move $x$ .

$\frac{2 (x \cdot x) + x \cdot - 3 - 4 (2 x) - 4 \cdot - 3 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Multiply $x$ by $x$ .

$\frac{2 x^{2} + x \cdot - 3 - 4 (2 x) - 4 \cdot - 3 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Move $- 3$ to the left of $x$ .

$\frac{2 x^{2} - 3 \cdot x - 4 (2 x) - 4 \cdot - 3 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Multiply $2$ by $- 4$ .

$\frac{2 x^{2} - 3 x - 8 x - 4 \cdot - 3 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Multiply $- 4$ by $- 3$ .

$\frac{2 x^{2} - 3 x - 8 x + 12 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Subtract $8 x$ from $- 3 x$ .

$\frac{2 x^{2} - 11 x + 12 + (2 x + 3) \cdot 2 x}{2 x (2 x - 3)}$

Apply the distributive property.

$\frac{2 x^{2} - 11 x + 12 + (2 x \cdot 2 + 3 \cdot 2) x}{2 x (2 x - 3)}$

Multiply $2$ by $2$ .

$\frac{2 x^{2} - 11 x + 12 + (4 x + 3 \cdot 2) x}{2 x (2 x - 3)}$

Multiply $3$ by $2$ .

$\frac{2 x^{2} - 11 x + 12 + (4 x + 6) x}{2 x (2 x - 3)}$

Apply the distributive property.

$\frac{2 x^{2} - 11 x + 12 + 4 x \cdot x + 6 x}{2 x (2 x - 3)}$

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

Move $x$ .

$\frac{2 x^{2} - 11 x + 12 + 4 (x \cdot x) + 6 x}{2 x (2 x - 3)}$

Multiply $x$ by $x$ .

$\frac{2 x^{2} - 11 x + 12 + 4 x^{2} + 6 x}{2 x (2 x - 3)}$

Add $2 x^{2}$ and $4 x^{2}$ .

$\frac{6 x^{2} - 11 x + 12 + 6 x}{2 x (2 x - 3)}$

Add $- 11 x$ and $6 x$ .

$\frac{6 x^{2} - 5 x + 12}{2 x (2 x - 3)}$

Simplify (x-4)/(2x)+(2x+3)/(2x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.