Final answer:
To solve the equation, combine like terms and isolate the variable h. Simplify the expression on the left side and find a common denominator on the right side. Rearrange the terms to get a quadratic equation and solve for h. Check for extraneous solutions.
Step-by-step explanation:
To solve the equation (1/h + 3) + (4/5) = h/4 - h, we need to combine like terms and isolate the variable h.
First, let's simplify the expression on the left side. The common denominator for 1/h and 4/5 is 5h. So, we have (5 + 3h)/5h + 4/5 = h/4 - h.
Next, let's find a common denominator for the fractions on the right side. The common denominator is 4. So, we have (5 + 3h)/5h + 4/5 = (h - 4h)/4. Now, we can combine the fractions and simplify the equation.
After simplifying and rearranging the terms, we get a quadratic equation: 12h^2 + 16h - 20 = 0. We can solve this equation using factoring, completing the square, or the quadratic formula.
Once we find the values for h, we can substitute them back into the original equation to check for extraneous solutions.