Solve for x and express your answer in simplest radical form

(4)/(x) - (3)/(x+1) = 7?

First you need to find a common denominator:
[ (4)/(x) * (x+1)/(x+1) ] - [ (3)/(x+1) * (x)/(x) ] = 7

(4x+4)/(x^2 +x) - (3x)/(x^2 +x) = 7

(4x+4-3x)/(x^2 +x) = 7

(x+4)/(x^2 +x) = 7

Now cross multiply:

x+4 = 7(x^2 +x)
x+4 = 7x^2 +7x

Bring everything accross to one side:
7x^2 +6x - 4 = 0

Then solve the quadratic (unless you have a clever calculator you need to use the quadratic formula)
x = -1.2975
x = 0.4404

x=(-sqrt(37)+3)/7 or (sqrt(37)-3)/7 (radical form)
x=-1.297538 or .440395 (decimal form)

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