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: Step 1: Combine the two fractions by multiplying the numerators and the denominators. ( 2+sqrt(7)3 ) ( 2-sqrt(7)3 ) = (2+sqrt(7))(2-sqrt(7))3 × 3 Step 2: Multiply the numerators using the difference of squares formula, (a+b)(a-b) = a^2 - b^2. Here, a=2 and b=sqrt(7). (2+sqrt(7))(2-sqrt(7)) = 2^2 - (sqrt(7))^2 = 4 - 7 = -3 Step 3: Multiply the denominators. 3 × 3 = 9 Step 4: Substitute the simplified numerator and denominator back into the fraction. (-3)/(9) Step 5: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. (-3 ÷ 3)/(9 ÷ 3) = (-1)/(3) The simplified expression is: -(1)/(3)