Question

if 3x/(x-a)(x-b)=2/x-a+1/x-b then a:b=​

Answer 1

Answer:

-2:1

Step-by-step explanation

Take LCM at RHS side

• 3x/(x-a)(x-b)=2(x-b)+1(x-a)/(x-a)(x-b)

• The denominators are common . SO cancle them

•  Then we get
• 3x=2(x-b)+(x-a)
• Now put x=a
• 3a=2(a-b)
• 3a=2a-2b
• 3a-2a=-2b
• a=-2b
• So,a/b=-2b/b
• a/b=-2/1
• Then a:b=-2:1 is your answer

Answer 2

a : b = (- 2) : 1

Step-by-step explanation:

Given, $\dfrac{3x}{(x-a)(x-b)}=\dfrac{2}{x-a}+\dfrac{1}{x-b}$

$\Rightarrow \dfrac{3x}{(x-a)(x-b)}=\dfrac{2(x-b)+1(x-a)}{(x-a)(x-b)}$

$\Rightarrow \dfrac{3x}{(x-a)(x-b)}=\dfrac{2x-2b+x-a}{(x-a)(x-b)}$

$\Rightarrow 3x=3x-a-2b$

• since $x\neq a,b$

$\Rightarrow a=-2b$

$\Rightarrow \dfrac{a}{b}=\dfrac{-2}{1}$

$\Rightarrow a:b=(-2):1$

So, a : b = (- 2) : 1

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