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Exercise

$\frac{x^2+x-2}{x^2+5x+6}$

Step-by-step Solution

1

Factor the trinomial $x^2+5x+6$ finding two numbers that multiply to form $6$ and added form $5$

$\begin{matrix}\left(2\right)\left(3\right)=6\\ \left(2\right)+\left(3\right)=5\end{matrix}$
2

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

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

Factor the trinomial $x^2+x-2$ finding two numbers that multiply to form $-2$ and added form $1$

$\begin{matrix}\left(-1\right)\left(2\right)=-2\\ \left(-1\right)+\left(2\right)=1\end{matrix}$
4

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

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

Simplify the fraction $\frac{\left(x-1\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$ by $x+2$

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

Final answer to the exercise

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

Try other ways to solve this exercise

  • Factor
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
  • Load more...
Can't find a method? Tell us so we can add it.

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Main Topic: Polynomial Factorization

They are a group of techniques that help us rewrite polynomial expressions as a product of factors.

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