Subjects algebra

Solve For H

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1. **State the problem:** We are given an equation involving terms with variable $h$: $$\frac{h}{21.0 + 1} + \frac{\frac{h}{21.0}}{21.0 + E} \times xos = gk$$ We want to simplify and solve for $h$ if possible. 2. **Simplify denominators:** Note that $21.0 + 1 = 22.0$, so the first term becomes: $$\frac{h}{22.0}$$ The second term is: $$\frac{\frac{h}{21.0}}{21.0 + E} = \frac{h}{21.0 \times (21.0 + E)}$$ 3. **Rewrite the equation:** $$\frac{h}{22.0} + \frac{h}{21.0 \times (21.0 + E)} \times xos = gk$$ 4. **Factor out $h$ on the left side:** $$h \left( \frac{1}{22.0} + \frac{xos}{21.0 \times (21.0 + E)} \right) = gk$$ 5. **Solve for $h$:** $$h = \frac{gk}{\frac{1}{22.0} + \frac{xos}{21.0 \times (21.0 + E)}}$$ 6. **Combine the denominator into a single fraction:** Find common denominator $22.0 \times 21.0 \times (21.0 + E)$: $$\frac{1}{22.0} = \frac{21.0 \times (21.0 + E)}{22.0 \times 21.0 \times (21.0 + E)}$$ $$\frac{xos}{21.0 \times (21.0 + E)} = \frac{22.0 \times xos}{22.0 \times 21.0 \times (21.0 + E)}$$ Sum: $$\frac{21.0 \times (21.0 + E) + 22.0 \times xos}{22.0 \times 21.0 \times (21.0 + E)}$$ 7. **Final expression for $h$:** $$h = \frac{gk \times 22.0 \times 21.0 \times (21.0 + E)}{21.0 \times (21.0 + E) + 22.0 \times xos}$$ This is the simplified formula for $h$ in terms of $gk$, $xos$, and $E$. **Answer:** $$h = \frac{gk \times 22.0 \times 21.0 \times (21.0 + E)}{21.0 \times (21.0 + E) + 22.0 \times xos}$$