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

Oct 18, 2017

Let's see.

#### Explanation:

Given,

$\frac{a}{x - 2} + \frac{b}{x + 3} = \frac{2 x + 11}{{x}^{2} + x - 6}$

Now find out the LCM of the LHS terms.

$\frac{a \left(x + 3\right) + b \left(x - 2\right)}{\left(x - 2\right) \left(x + 3\right)} = \frac{2 x + 11}{{x}^{2} + x - 6}$

$\frac{a \left(x + 3\right) + b \left(x - 2\right)}{\left(x - 2\right) \left(x + 3\right)} = \frac{2 x + 11}{\left(x - 2\right) \left(x + 3\right)}$

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

$a \left(x + 3\right) + b \left(x - 2\right) = 2 x + 11$

$a x + b x + 3 a - 2 b = 2 x + 11$

$\textcolor{red}{\left(a + b\right) x + \left(3 a - 2 b\right) = 2 x + 11}$.

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

$\textcolor{red}{a + b = 2}$..........(1).

$\textcolor{red}{3 a - 2 b = 11}$..........(2).

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

Hope it Helps:)