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

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

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

Multiply by $1$ .

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

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

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