Simplify (15x-3)/(5x^2-11x+2)+(x-5)/(2x^2-11x+5)

$\frac{15 x - 3}{5 x^{2} - 11 x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Simplify each term.

Factor $3$ out of $15 x - 3$ .

Factor $3$ out of $15 x$ .

$\frac{3 (5 x) - 3}{5 x^{2} - 11 x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Factor $3$ out of $- 3$ .

$\frac{3 (5 x) + 3 (- 1)}{5 x^{2} - 11 x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

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

$\frac{3 (5 x - 1)}{5 x^{2} - 11 x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot 2 = 10$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$\frac{3 (5 x - 1)}{5 x^{2} - 11 (x) + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Rewrite $- 11$ as $- 1$ plus $- 10$

$\frac{3 (5 x - 1)}{5 x^{2} + (- 1 - 10) x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Apply the distributive property.

$\frac{3 (5 x - 1)}{5 x^{2} - 1 x - 10 x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{3 (5 x - 1)}{(5 x^{2} - 1 x) - 10 x + 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Factor out the greatest common factor (GCF) from each group.

$\frac{3 (5 x - 1)}{x (5 x - 1) - 2 (5 x - 1)} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Factor the polynomial by factoring out the greatest common factor, $5 x - 1$ .

$\frac{3 (5 x - 1)}{(5 x - 1) (x - 2)} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Cancel the common factor of $5 x - 1$ .

Cancel the common factor.

$\frac{3 (5 x - 1)}{(5 x - 1) (x - 2)} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Rewrite the expression.

$\frac{3}{x - 2} + \frac{x - 5}{2 x^{2} - 11 x + 5}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 5 = 10$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$\frac{3}{x - 2} + \frac{x - 5}{2 x^{2} - 11 (x) + 5}$

Rewrite $- 11$ as $- 1$ plus $- 10$

$\frac{3}{x - 2} + \frac{x - 5}{2 x^{2} + (- 1 - 10) x + 5}$

Apply the distributive property.

$\frac{3}{x - 2} + \frac{x - 5}{2 x^{2} - 1 x - 10 x + 5}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{3}{x - 2} + \frac{x - 5}{(2 x^{2} - 1 x) - 10 x + 5}$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

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

Cancel the common factor of $x - 5$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $3$ .

$\frac{6 x + 3 \cdot - 1 + x - 2}{(2 x - 1) (x - 2)}$

Multiply $3$ by $- 1$ .

$\frac{6 x - 3 + x - 2}{(2 x - 1) (x - 2)}$

Add $6 x$ and $x$ .

$\frac{7 x - 3 - 2}{(2 x - 1) (x - 2)}$

Subtract $2$ from $- 3$ .

$\frac{7 x - 5}{(2 x - 1) (x - 2)}$

Simplify (15x-3)/(5x^2-11x+2)+(x-5)/(2x^2-11x+5)

Related Questions

Support LCMGCF.com by disabling your adblocker.