Answer:
Suppose we have an equation like:
[tex]\frac{A}{C} = \frac{B}{D}[/tex]
If we want to remove the denominators, we should multiply both sides by each denominator.
First, let's multiply both sides by C.
[tex]\frac{A}{C}*C = \frac{B}{D}*C[/tex]
[tex]A = \frac{B}{D}*C[/tex]
Now let's multiply both sides by D.
[tex]A*D = \frac{B}{D}*C*D[/tex]
[tex]A*D = B*C[/tex]
So now we removed the denominators.
Now let's do this to our expression.
[tex]2 - \frac{3}{4*x} = \frac{9}{10}[/tex]
First, let's multiply both sides by 10
[tex](2 - \frac{3}{4*x})*10 = \frac{9}{10}*10[/tex]
[tex]20 + \frac{30}{4*x} = 9[/tex]
Now let's multiply both sides by 4*x
[tex](20 + \frac{30}{4*x})*4*x = 9*4*x[/tex]
[tex]20*4*x - 30 = 9*4*x[/tex]
[tex]80*x - 30 = 36*x[/tex]
Now we can solve this for x:
[tex]80*x - 36*x = 30[/tex]
[tex]44*x = 30[/tex]
[tex]x = \frac{30}{44} = 0.68[/tex]
