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

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

Step 1

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

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

Rewrite $1$ as $- 2$ plus $3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 2

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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