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DiKsa [7]
2 years ago
13

Simplify quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2 x2 + 1 x2 − 1 x + 3 x − 3

Mathematics
1 answer:
Marina CMI [18]2 years ago
7 0

Answer:

\frac{x^2+5x+6}{x+2}

⇒ x+3

Step-by-step explanation:

To simplify:

\frac{x^2+5x+6}{x+2}

To simplify the given expression we need to factor the numerator.

We have

x^2+5x+6

Using split the middle term method by splitting 5x into two terms ax and bx such that ax+bx=5x and ax(bx)=6x^2

We see that [ax=2x and bx=3x]

Thus we can write

⇒ x^2+2x+3x+6

Factoring in pairs by taking the GCF of terms in pairs.

⇒ x(x+2)+3(x+2)

Factoring the whole expression as (x+2)is a common factor.

⇒ (x+2)(x+3)

Now, the expression can be rewritten as:

\frac{(x+2)(x+3)}{x+2}  

Canceling out the common expressions, we have.

⇒ x+3

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