Question

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

Answer 1

Answer:

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)

Answer 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,

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

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