Pre-Algebra Examples

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

Step 1

Factor by grouping.

Tap for more steps...

Step 1.1

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 $b = 3$ .

Tap for more steps...

Step 1.1.1

Factor $3$ out of $3 x$ .

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

Step 1.1.2

Rewrite $3$ as $- 2$ plus $5$

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

Step 1.1.3

Apply the distributive property.

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

Step 1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.2.1

Group the first two terms and the last two terms.

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

Step 1.2.2

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

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

Step 1.3

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

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

Step 2

Cancel the common factor of $x - 1$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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