Solve for $$ \mathrm{x}: \quad M=\frac{a b x}{x+y} $$

Question

UpStudy AI · Accepted Answer

To solve for $$ x $$ in the equation:

$$
M = \frac{a b x}{x + y}
$$

follow these steps:

1. **Multiply both sides by $$ (x + y) $$ to eliminate the denominator:**

$$
   M(x + y) = a b x
   $$

2. **Distribute $$ M $$ on the left side:**

$$
   Mx + My = a b x
   $$

3. **Rearrange the equation to gather terms involving $$ x $$ on one side:**

$$
   Mx - a b x = -My
   $$

4. **Factor out $$ x $$ from the left side:**

$$
   x(M - a b) = -My
   $$

5. **Solve for $$ x $$ by dividing both sides by $$ (M - a b) $$:**

$$
   x = \frac{-My}{M - a b}
   $$

6. **Simplify the negative signs:**

$$
   x = \frac{My}{a b - M}
   $$

**Final Solution:**

$$
x = \frac{M \cdot y}{a b - M}
$$
$$ x = \frac{M \cdot y}{a b - M} $$

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