(b) Make e the subject of $$ w=\sqrt{\frac{e+g}{e f-d}} $$

Question

UpStudy AI · Accepted Answer

1. Start with the given equation:
   $$
   w = \sqrt{\frac{e+g}{ef-d}}
   $$

2. Square both sides to eliminate the square root:
   $$
   w^2 = \frac{e+g}{ef-d}
   $$

3. Multiply both sides by $$(ef-d)$$ to get:
   $$
   w^2(ef-d) = e+g
   $$

4. Distribute $$w^2$$ on the left-hand side:
   $$
   w^2ef - w^2d = e+g
   $$

5. Bring all terms involving $$e$$ to one side:
   $$
   w^2ef - e = w^2d + g
   $$

6. Factor $$e$$ from the left-hand side:
   $$
   e(w^2f-1) = w^2d + g
   $$

7. Finally, solve for $$e$$ by dividing both sides by $$(w^2f-1)$$:
   $$
   e = \frac{w^2d+g}{w^2f-1}
   $$
$$ e = \frac{w^2d + g}{w^2f - 1} $$

(b) Make e the subject of