3/4=9/x+8

To solve the equation \( \frac{3}{4} = \frac{9}{x} + 8 \), follow these steps:

1. Let's isolate the fraction \( \frac{9}{x} \) on one side of the equation: \[ \frac{3}{4} - 8 = \frac{9}{x} \]

2. To combine \( \frac{3}{4} \) and \( 8 \), convert \( 8 \) into a fraction with a denominator of \( 4 \): \[ 8 = \frac{32}{4} \] Therefore: \[ \frac{3}{4} - \frac{32}{4} = \frac{3 - 32}{4} = \frac{-29}{4} \]

3. Now, the equation becomes: \[ \frac{-29}{4} = \frac{9}{x} \]

4. Cross-multiply to eliminate the fractions: \[ -29x = 36 \]

5. Now, solve for \( x \): \[ x = \frac{36}{-29} = -\frac{36}{29} \]

So, the solution for \( x \) is: \[ x = -\frac{36}{29} \]