Simplify the expression: (3)/(x+1) − (2)/(x+2)

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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) = x² + 2x + x + 2 = x² + 3x + 2 So, the expression can also be written as: (x+4)/(x²+3x+2) The expression in its simplest form is: (x+4)/((x+1)(x+2))

Simplify the expression: (3)/(x+1) - (2)/(x+2)

Answer

Step-by-step solution

Identify the expression to simplify.

Find a common denominator for the two fractions.

Rewrite each fraction with the common denominator.

Subtract the fractions.

Expand the numerator.

Simplify the numerator by combining like terms.

Write the simplified expression as a single fraction.

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