Question

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

Answer 1

9514 1404 393

Answer:

x = -6/11

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