This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to the problem. (36x^2 - 9y^2)/(4xy) - (20xy)/(6x - 3y) Step 1: Factor the expressions in the numerators and denominators. The numerator of the first fraction is a difference of squares after factoring out 9: 36x^2 - 9y^2 = 9(4x^2 - y^2) = 9((2x)^2 - y^2) = 9(2x-y)(2x+y) The denominator of the second fraction can be factored: 6x - 3y = 3(2x - y) Step 2: Rewrite the expression with the factored terms. (9(2x-y)(2x+y))/(4xy) - (20xy)/(3(2x - y)) Step 3: Determine the least common denominator (LCD) for the two fractions. The denominators are 4xy and 3(2x-y). The LCD is 12xy(2x-y). Step 4: Rewrite each fraction with the LCD. For the first fraction, multiply the numerator and denominator by 3(2x-y): (9(2x-y)(2x+y))/(4xy) × (3(2x-y))/(3(2x-y)) = (27(2x-y)^2(2x+y))/(12xy(2x-y)) For the second fraction, multiply the numerator and denominator by 4xy: (20xy)/(3(2x - y)) × (4xy)/(4xy) = (80x^2y^2)/(12xy(2x-y)) Step 5: Subtract the fractions. (27(2x-y)^2(2x+y))/(12xy(2x-y)) - (80x^2y^2)/(12xy(2x-y)) = (27(2x-y)^2(2x+y) - 80x^2y^2)/(12xy(2x-y)) The simplified expression is (27(2x-y)^2(2x+y) - 80x^2y^2)/(12xy(2x-y)). Last free one today — make it count tomorrow, or type /upgrade for unlimited.