what is the difference?\n\\( \\frac { x } { x ^ { 2 } + 3 x + 2 } - \\frac { 1 } { ( x + 2 ) ( x + 1 ) } \\)
what is the difference?\n\\( \\frac { x } { x ^ { 2 } + 3 x + 2 } - \\frac { 1 } { ( x + 2 ) ( x + 1 ) } \\)
Answer
Explanation:
Step1: Factor the denominator
Factor (x^{2}+3x + 2=(x + 1)(x+2)). The expression becomes (\frac{x}{(x + 1)(x + 2)}-\frac{1}{(x + 2)(x + 1)}).
Step2: Subtract the fractions
Since the denominators are the same, we subtract the numerators: (\frac{x-1}{(x + 1)(x + 2)}). Simplify ((x + 1)(x + 2)=x^{2}+3x + 2). So the result is (\frac{x - 1}{x^{2}+3x + 2}).
Answer:
(\frac{x - 1}{x^{2}+3x + 2})