Question

x+3/x-3 + x+2/x-2 =2


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Answer 1

ANSWER:

Given:

• [(x+3)/(x-3)] + [(x+2)/(x-2)]= 2

To Find:

• Value of x

Solution:

$:\longrightarrow \sf{\dfrac{x+3}{x-3} + \dfrac{x+2}{x-2} = 2} \\\\\text{Taking LCM,} \\\\:\implies \sf{\dfrac{(x+3)*(x-2) + (x-3)*(x+2)}{(x-3)*(x-2)} = 2} \\\\:\implies\sf{\dfrac{(x^2 + {3x\!\!\!/} - {2x\!\!\!/} - 6 + x^2 - {3x\!\!\!/} + {2x\!\!\!/} - 6)}{(x^2-3x-2x+6)} = 2} \\\\:\implies \sf{2x^2 - 12 = 2*(x^2 - 5x + 6)} \\\\:\implies \sf{{2\!\!\!/}*(x^2 - 6) = {2\!\!\!/}*(x^2-5x+6)} \\\\:\implies \sf{{x^2\!\!\!\!/}-6= {x^2\!\!\!\!/}- 5x+6} \\\\:\implies \sf{5x = 12} \\\\:\implies \bf{x = \dfrac{12}{5}}$