Simplify (2x^2-5x+3)/(x^2+5x-6)

2×2-5x+3×2+5x-6
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅3=6 and whose sum is b=-5.
Factor -5 out of -5x.
2×2-5(x)+3×2+5x-6
Rewrite -5 as -2 plus -3
2×2+(-2-3)x+3×2+5x-6
Apply the distributive property.
2×2-2x-3x+3×2+5x-6
2×2-2x-3x+3×2+5x-6
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(2×2-2x)-3x+3×2+5x-6
Factor out the greatest common factor (GCF) from each group.
2x(x-1)-3(x-1)x2+5x-6
2x(x-1)-3(x-1)x2+5x-6
Factor the polynomial by factoring out the greatest common factor, x-1.
(x-1)(2x-3)x2+5x-6
(x-1)(2x-3)x2+5x-6
Factor x2+5x-6 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is 5.
-1,6
Write the factored form using these integers.
(x-1)(2x-3)(x-1)(x+6)
(x-1)(2x-3)(x-1)(x+6)
Cancel the common factor of x-1.
Cancel the common factor.
(x-1)(2x-3)(x-1)(x+6)
Rewrite the expression.
2x-3x+6
2x-3x+6
Simplify (2x^2-5x+3)/(x^2+5x-6)