Answer :

If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) , then the result is (12 - 5x)/(x - 3) .

The sum of the algebraic expressions 3/(5x-15) and (x+3)/(x-3) are written as ; ⇒ 3/(5x-15) + (x+3)/(x-3) ;

taking 5 common from the denominator of the first term ,

we get ;

⇒ 3/5(x-3) + (x+3)/(x-3) ;

taking LCM as 5(x-3) and simplifying further ,

we have ;

⇒ 3/5(x-3) + (x+3)/(x-3) ;

⇒ [3 + 5(x+3)]/5(x-3) ;

⇒ (5x + 18)/5(x-3) .......equation(1)

Now 6x/(x²-3x) is subtracted from the equation(1)

⇒ (5x + 18)/5(x-3) - 6x/(x²-3x) ;

⇒ (5x + 18)/5(x-3) - 6x/x(x-3) ;

⇒ (5x + 18)/5(x-3) - 6/(x-3) ;

taking LCM as as 5(x-3) and simplifying further ,

we have ;

⇒ (5x + 18 - 30)/5(x-3) ;

⇒ (5x -12)/5(x-3) ;

Therefore , the final result is (5x -12)/5(x-3) .

The given question is incomplete , the complete question is

If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) . What is the result ?

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