Question

Solution to 3/x + 2/(x+1) = 3/5x?

Answer 1

9514 1404 393

Answer:

  x = -6/11

Step-by-step explanation:

We assume you want the solution to ...

  3/x +2/(x+1) = 3/(5x)

Subtracting the term on the right, we get the form f(x) = 0.

  $\displaystyle\frac{3}{x}+\frac{2}{x+1}-\frac{3}{5x}=0\\\\\frac{15-3}{5x}+\frac{2}{x+1}=0\\\\\frac{12(x+1)+10x}{5x(x+1)}=0\\\\22x+12=0\quad\text{numerator must be zero}\\\\x+\frac{6}{11}=0\quad\text{divide by 22, simplify}\\\\\boxed{x=-\frac{6}{11}}$

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If you really intend 3/x +2/(x+1) = (3/5)x as you have written, the solution is 3 irrational values for x. I find a graphing calculator a convenient way to find them.