Question

how to solve this problem?

Answer 1

I'm not sure how you should do it, if this isn't how it is suppose to look like then let me know.

$\frac{9}{4x} + \frac{x + 3}{4x} =\frac{3}{2x}$

Because the denominators are the same(4x), you can add the 2 fractions together:

$\frac{9}{4x} + \frac{x + 3}{4x} =\frac{3}{2x}$

$\frac{9+x+3}{4x} =\frac{3}{2x}$

$\frac{12 +x}{4x} =\frac{3}{2x}$

Now you can cross multiply, which is just multiplying 2x on both sides, and multiplying 4x on both sides

$(2x)\frac{12+x}{4x} =\frac{3}{2x} (2x)$

$(4x)\frac{2x(12+x)}{4x} =3(4x)$

2x(12 + x) = 3(4x)  Multiply 2x into (12 + x), and multiply 3 into (4x)

24x + 2x² = 12x Subtract 12x on both sides

12x + 2x² = 0 Factor out 2x

2x (6 + x) = 0

2x = 0 Divide 2 on both sides

x = 0

6 + x = 0 Subtract 6 on both sides

x = -6

Or:

$\frac{9}{4x} +\frac{x + 3}{4x} =\frac{3}{2x}$

$\frac{12 + x}{4x} =\frac{3}{2x}$  Subtract 3/2x on both sides

$\frac{12 +x}{4x} -\frac{3}{2x} =0$  Make the denominators the same

$\frac{12+x}{4x} -\frac{6}{4x} =0$

$\frac{6+x}{4x} = 0$ Multiply 4x on both sides

6 + x = 0  Subtract 6 on both sides

x = -6

Answer 2

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