Simplify (5x-1)/(x^2-3x+2)+3/(2x-4)

$\frac{5 x - 1}{x^{2} - 3 x + 2} + \frac{3}{2 x - 4}$

Simplify each term.

Factor $x^{2} - 3 x + 2$ using the AC method.

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 $2$ and whose sum is $- 3$ .

$- 2, - 1$

Write the factored form using these integers.

$\frac{5 x - 1}{(x - 2) (x - 1)} + \frac{3}{2 x - 4}$

Factor $2$ out of $2 x - 4$ .

Factor $2$ out of $2 x$ .

$\frac{5 x - 1}{(x - 2) (x - 1)} + \frac{3}{2 (x) - 4}$

Factor $2$ out of $- 4$ .

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

Factor $2$ out of $2 x + 2 \cdot - 2$ .

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

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

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

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

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

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

Multiply $\frac{5 x - 1}{(x - 2) (x - 1)}$ by $\frac{2}{2}$ .

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

Multiply $\frac{3}{2 (x - 2)}$ by $\frac{x - 1}{x - 1}$ .

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

Reorder the factors of $(x - 2) (x - 1) \cdot 2$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $5$ .

$\frac{10 x - 1 \cdot 2 + 3 (x - 1)}{2 (x - 1) (x - 2)}$

Multiply $- 1$ by $2$ .

$\frac{10 x - 2 + 3 (x - 1)}{2 (x - 1) (x - 2)}$

Apply the distributive property.

$\frac{10 x - 2 + 3 x + 3 \cdot - 1}{2 (x - 1) (x - 2)}$

Multiply $3$ by $- 1$ .

$\frac{10 x - 2 + 3 x - 3}{2 (x - 1) (x - 2)}$

Add $10 x$ and $3 x$ .

$\frac{13 x - 2 - 3}{2 (x - 1) (x - 2)}$

Subtract $3$ from $- 2$ .

$\frac{13 x - 5}{2 (x - 1) (x - 2)}$

Simplify (5x-1)/(x^2-3x+2)+3/(2x-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.