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Wittaler [7]
3 years ago
6

WILL MARK BRAINLIEST ASAP!!

Mathematics
2 answers:
7nadin3 [17]3 years ago
3 0

\dfrac{x^2+ax-4}{x+2}+\dfrac{x+b}{x+2}=\dfrac{x^2+ax-4+x+b}{x+2}=\dfrac{x^2+(a+1)x+(b-4)}{x+2}\\\\\dfrac{x^2+(a+1)x+(b-4)}{x+2}=x+1\\\\\dfrac{x^2+(a+1)x+(b-4)}{x+2}=\dfrac{(x+1)(x+2)}{x+2}\\\\\dfrac{x^2+(a+1)x+(b-4)}{x+2}=\dfrac{(x)(x)+(x)(2)+(1)(x)+(1)(2)}{x+2}\\\\\dfrac{x^2+(a+1)x+(b-4)}{x+2}=\dfrac{x^2+2x+x+2}{x+2}\\\\\dfrac{x^2+(a+1)x+(b-4)}{x+2}=\dfrac{x^2+3x+2}{x+2}\iff a+1=3\ \wedge\ b-4=2\\\\\boxed{a=2\ \wedge\ b=6}

lubasha [3.4K]3 years ago
3 0

Answer:

The correct choice for <em>a</em> and <em>b</em> is 2 and 6 respectively.

Step-by-step explanation:

\frac{x^{2}+ax-4}{x+2}+\frac{x+b}{x+2}

The least common multiple in the provided expression is x+2. Therefore, the above expression can be written as:

\frac{x^{2}+ax-4+x+b}{x+2}

Arrange the like terms together as shown:

\frac{x^{2}+ax+x-4+b}{x+2}=\frac{x^{2}+x(a+1)+b-4}{x+2}

It is given that after simplified her answer was x+1. Therefore, this information can be written as:

\frac{x^{2}+x(a+1)+b-4}{x+2}= x+1

Multiply numerator and denominator by x+2 we get,

\frac{x^{2}+x(a+1)+b-4}{x+2}= \frac{(x+1)(x+2)}{x+2}

Further simplify,

\frac{x^{2}+x(a+1)+b-4}{x+2}= \frac{(x^{2}+2x+x+2)}{x+2}

Add the like terms:

\frac{x^{2}+x(a+1)+b-4}{x+2}= \frac{(x^{2}+3x+2)}{x+2}

Now compare the coefficient of x term and constant term.

a+1=3 and b-4=2

further solve:

a=2 and b=6

Hence, the correct choice for <em>a</em> and <em>b</em> is 2 and 6 respectively.

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