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13 votes
13 votes
2- x+2/x-3 - x-6/x+3

A=
B=

It can be written in the form is like ax+b/x^2-9
so we only need the A and B.

Please reply to this ASAP

User Nick Mowen
by
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1 Answer

12 votes
12 votes

Explanation:

so, if I understand your text correctly, we need to bring

2 - (x+2)/(x-3) - (x-6)/(x+3)

into a form

(ax + b)/(x² - 9)

what we notice immediately is

(x+3)(x-3) = x² - 9

that makes sense, as we want to transform all terms into fractions with the same denominator.

and the necessary "criss-cross" multiplication leads to (x² -9) as denominator.

so, let's transform every term to a fraction with that denominator, and then we add or subtract them all up as per the original expression.

2 :

multiply by (x²-9)/(x²-9)

2(x²-9)/(x²-9) = (2x²-18)/(x²-9)

(x+2)/(x-3) :

multiply by (x+3)/(x+3)

(x+2)(x+3)/(x²-9) = (x²+3x+2x+6)/(x²-9) =

= (x²+5x+6)/(x²-9)

(x-6)/(x+3) :

multiply by (x-3)/(x-3)

(x-6)(x-3)/(x²-9) = (x²-3x-6x+18)/(x²-9) =

= (x²-9x+18)/(x²-9)

for the whole expression we get then

(2x²-18)/(x²-9) - (x²+5x+6)/(x²-9) - (x²-9x+18)/(x²-9) =

= (2x²-x²-x² -5x+9x -18-6-18)/(x²-9) =

= ( 0 + 4x - 42 )/(x²-9)

a = 4

b = -42

User Ronen Yacobi
by
3.1k points