Solve. 6/x + x/2 = 4
6/x + x/2 = 4
I just can't seem to figure it out.
Start by eliminating the fractions. To do that, multiply by
the common denominator. Find the common denominator
by multiplying the two denominators: 2 * x = 2x.
6/x + x/2 = 4
2x (6/x) + 2x (x/2) = 2x * 4
12 + x^2 = 8x
12 + x^2 - 8x = 0
x^2 - 8x + 12 = 0
We need factors of 12 which, when added together,
will give 8. 6 and 2 satisfiy the requirements.
(x - 6) (x - 2) = 0
One or both factors must equal zero.
x - 6 = 0
x = 6
or
x - 2 = 0
x = 2
Try them in the original equation.
First, 6:
6/x + x/2 = 4
6/6 + 6/2 = 4
1 + 3 = 4
Now, 2:
6/x + x/2 = 4
6/2 + 2/2 = 4
3 + 1 = 4
Plotting this equation gives a parabola which
crosses the x-axis at (2, 0) and (6, 0)