Question

How do you solve `x+ 8- \frac{20}{x} = 0`?

Answer 1

`x=+2" and "x=-10`

Explanation:

Given:`" "x+8-20/x=0`

We need to remove `x` as a denominator.

`color(brown)("This is one approach. dc shows another approach.")`
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Add `20/x` to both sides isolating the term `20/x`

`x+8=20/x`

Multiply both sides by `x`

`x(x+8)=20xx x/x`

`x^2+8x=20`

Subtract 20 from both sides

`x^2+8x-20=0 larr" now we have our quadratic equation"`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that `2xx10=20" and "10-2=8` so we must have the form:

`(x-2)(x+10)=0" "` as `(-2)xx10 = -20` as required

Thus the 2 solutions are: `x=+2" and "x=-10`