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
Step 1: Identify the expression to simplify. The expression is given as: (3)/(x+1) - (2)/(x+2) Step 2: Find a common denominator for the two fractions. The common denominator is the product of the individual denominators: (x+1)(x+2). Step 3: Rewrite each fraction with the common denominator. To get the common denominator for the first fraction, multiply its numerator and denominator by (x+2): (3)/(x+1) = (3(x+2))/((x+1)(x+2)) To get the common denominator for the second fraction, multiply its numerator and denominator by (x+1): (2)/(x+2) = (2(x+1))/((x+1)(x+2)) Step 4: Subtract the fractions. Now that both fractions have the same denominator, subtract their numerators: (3(x+2))/((x+1)(x+2)) - (2(x+1))/((x+1)(x+2)) = (3(x+2) - 2(x+1))/((x+1)(x+2)) Step 5: Expand the numerator. Distribute the numbers into the parentheses in the numerator: 3(x+2) - 2(x+1) = (3x + 6) - (2x + 2) Step 6: Simplify the numerator by combining like terms. 3x + 6 - 2x - 2 = (3x - 2x) + (6 - 2) = x + 4 Step 7: Write the simplified expression as a single fraction. (x+4)/((x+1)(x+2)) The denominator can also be expanded: (x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2 So, the expression can also be written as: (x+4)/(x^2+3x+2) The expression in its simplest form is: (x+4)/((x+1)(x+2)) Send me the next one 📸