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  • Find the roots of the following equations: (ii) 1 / x + 4 - 1 / x - 7 = 11 / 30 x not equals - 4, 7

Q3.    Find the roots of the following equations:

                (ii)    \frac{1}{x+4} - \frac{1}{x- 7} = \frac{11}{30},\ x\neq -4,7

Answers (1)

best_answer

Given equation: \frac{1}{x+4} - \frac{1}{x- 7} = \frac{11}{30},\ x\neq -4,7

So, simplifying it,

\Rightarrow \frac{x-7-x-4}{(x+4)(x-7)} = \frac{11}{30}

\Rightarrow \frac{-11}{(x+4)(x-7)} = \frac{11}{30}

\Rightarrow (x+4)(x-7) = -30

\Rightarrow x^2-3x-28 = -30    or    \Rightarrow x^2-3x+2 = 0

Can be written as:

\Rightarrow x^2-x-2x+2 = 0

\Rightarrow x(x-1) -2(x-1) = 0

\Rightarrow (x-2)(x-1) = 0

Hence the roots of the given equation are:

\Rightarrow x = 1\ or\ 2

Posted by

Divya Prakash Singh

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