# What is the difference? StartFraction x Over x squared + 3 x + 2 EndFraction minus StartFraction 1 Over (x + 2) (x + 1) EndFraction options A)StartFraction x minus 1 Over 6 x + 4 EndFraction B)StartFraction negative 1 Over 4 x + 2 EndFraction C)StartFraction 1 Over x + 2 EndFraction D)StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction

• Subject:

Mathematics
• Author:

silky
• Created:

7 months ago

D

Step-by-step explanation:

x/(x²+3x+2) - 1/[(x+2)(x+1)]

x² + 3x + 2 = x² + 2x + x + 2

= x(x + 2) + (x + 2)

= (x + 2)(x + 1)

= x/[(x+2)(x+1)] - 1/[(x+2)(x+1)]

= (x-1)/[(x+2)(x+1)]

= (x-1)/(x²+3x+2)

The difference of rational polynomial function is \frac{x-1}{x^{2} +3x+2}

Given expression is,

\frac{x}{x^{2} +3x+2}-\frac{1}{(x+2)(x+1)}

(x+2)(x+1)=x^{2} +2x+x+2=x^{2} +3x+2

Given expression can be written as,

\frac{x}{x^{2} +3x+2}-\frac{1}{x^{2} +3x+2} =\frac{x-1}{x^{2} +3x+2}

Answer: D)StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction Explanation: The difference between the two fractions can be found by subtracting the numerators and denominators from each other. The numerator of the first fraction is "x" and the numerator of the second fraction is "1". Therefore, the difference is "x-1". The denominator of the first fraction is "x^2+3x+2" and the denominator of the second fraction is "(x+2)(x+1)". Simplifying, this becomes "x^2+3x+2". Therefore, the difference in the denominator is also "x^2+3x+2". As such, the difference is "StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction".

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