ration equations?

Question

(x+10)/(x^2-2)=4/x

Answer 1

(x + 10) / (x^2 - 2) = 4/x

To solve this, we cross multiply; numerator of left hand side times denominator of right hand side, equals denominator of left hand side times numerator of right hand side.

x(x + 10) = 4(x^2 - 2)

Now, expand both sides, to obtain

x^2 + 10x = 4x^2 - 8

Move everything to the right hand side,

0 = 3x^2 - 10x - 8

Factor.

0 = (3x + 2) (x - 4)

And solve normally.

3x + 2 = 0, means x = -2/3
x - 4 = 0, means x = 4