How do you simplify the rational expression: (x+2)/(4x-8)(3x-9)/(x+4)(2x-21)/(x^2-x-6)x+24x−83x−9x+42x−21x2−x−6?
1 Answer
Explanation:
The idea is to factor out numbers is the first-degree polynomial (if possible), and to factor the highest-degree, finding their roots (if possible). So, let's work separately on the three pieces:
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First fraction:
Numerator:x+2->x+2→ nothing to do;
**Denominator:4x-8->4x−8→ can factor a44 , obtaining4(x-2)4(x−2) . -
Second fraction:
Numerator:3x-9->3x−9→ can factor a33 , obtaining3(x-3)3(x−3) ;
**Denominator:x+4->x+4→ nothing to do. -
First fraction:
Numerator:2x-21->2x−21→ nothing to do;
**Denominator:x^2-x-6->x2−x−6→ its roots are33 and-2−2 , so we can write it as(x-3)(x+2)(x−3)(x+2) .
Writing back the whole expression with this changes gives