Question - Solving an Equation Involving Fractions
Solution:
Here are the steps to solve the given equation:1. Simplify the left side of the equation: $$ 4 \frac{5}{x+y} = 4 + \frac{20}{x+y} $$2. Equate the left side to the right side: $$ 4 + \frac{20}{x+y} = \frac{25x+y}{x+y} $$3. Multiply both sides by $$ x+y $$ to clear the fraction: $$ (4 + \frac{20}{x+y})(x+y) = (25x+y) $$4. Expand and simplify: $$ 4(x+y) + 20 = 25x+y $$5. Distribute the 4: $$ 4x + 4y + 20 = 25x+y $$6. Move terms of x and y to one side: $$ 4x - 25x + 4y - y = -20 $$7. Combine like terms: $$ -21x + 3y = -20 $$8. Divide by -21: $$ x = \frac{3y + 20}{21} $$The answer is $$ x = \frac{3y + 20}{21} $$.
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