Question

For f(x)=x+6/x-3 find all real numbers x, where f(x)=5/2

Answer 1

x = 9

Explanation:

You want the values of x that make f(x) = (x +6)/(x -3) equal to 5/2.

Solution

You want ...

`(x+6)/(x-3)=(5)/(2)\\\\\\2(x+6)=5(x-3)\qquad\text{multiply by $2(x-3)$}\\\\2x+12=5x-15\qquad\text{eliminate parentheses}\\\\27=3x\qquad\text{add $15-2x$}\\\\\boxed{9=x}\qquad\text{divide by 3}`

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Additional comment

There is only one solution.

The equation can be rewritten as ...

1+(9/(x-3))=5/2
9/(x-3)=3/2=9/6
x -3 = 6

Then x=6+3=9.

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