If a/(x-2)+b/(x+3)=(2x+11)/(x^2+x-6) then (a,b) = ?

1 Answer
Oct 18, 2017

Let's see.

Explanation:

Given,

a/(x-2) +b/(x+3)=(2x+11)/(x^2+x-6)

Now find out the LCM of the LHS terms.

(a(x+3)+b(x-2))/((x-2)(x+3))=(2x+11)/(x^2+x-6)

(a(x+3)+b(x-2))/((x-2)(x+3))=(2x+11)/((x-2)(x+3))

Now, simplifying the equation by multiplying both the sides by the denominator and then addind the remaining terms in numerator, we get rarr

a(x+3)+b(x-2)=2x+11

ax+bx+3a-2b=2x+11

color(red)((a+b)x+(3a-2b)=2x+11).

Now, comparing the coefficients of x & x^0, we get two more equations:

color(red)(a+b=2)..........(1).

color(red)(3a-2b=11)..........(2).

Now, solve the respective equations to get the values of a & b.

Hope it Helps:)