Question

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

Answer 1

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:)