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.
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5. (b) Simplify (x-y)/(y+x) ÷ (y-x)/(x+y). Step 1: Rewrite the division as multiplication by the reciprocal. Dividing by a fraction is equivalent to multiplying by its reciprocal. (x-y)/(y+x) ÷ (y-x)/(x+y) = (x-y)/(y+x) × (x+y)/(y-x) Step 2: Recognize common factors and relationships between terms. Notice that y+x is the same as x+y. Also, y-x is the negative of x-y, i.e., y-x = -(x-y). Substitute these into the expression: (x-y)/(x+y) × (x+y)/(-(x-y)) Step 3: Cancel out common terms. The (x+y) in the denominator of the first fraction cancels with the (x+y) in the numerator of the second fraction. The (x-y) in the numerator of the first fraction cancels with the (x-y) in the denominator of the second fraction. (x-y)(x+y) × (x+y)-(x-y) This leaves: 1 × (1)/(-1) Step 4: Perform the final multiplication. 1 × (-1) = -1 The simplified expression is: -1 Got more? Send 'em.