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:)