{1+x+xy+x²y}{3+2x-x²} is equal to

Correct Answer is : 1+xy3−x1+xy/3-x3−x1+xy

Correct Answer is : 1+xy3−x1+xy/3-x3−x1+xy

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CTET Paper II (Mathematics and Science) 23 Dec 2021 Solved Paper

Question : 42 of 150

Marks: +1, -0

\frac{1+x+xy+x^{2}y}{3+2x-x^{2}}

is equal to

Solution:

Concept:

Factor the numerator and denominator to simplify the rational expression.

Explanation:

First, factor the numerator:

1 + x + xy + x^2y = (1+x) + xy(1+x) = (1+x)(1+xy)

Next, factor the denominator:

3 + 2x - x^2 = -(x^2 - 2x - 3) = -(x-3)(x+1)

Now, the expression becomes

\frac{(1+x)(1+xy)}{-(x-3)(x+1)}

Cancel the common factor

(1+x)

(provided

x \neq -1

). This gives

\frac{1+xy}{-(x-3)} = \frac{1+xy}{3-x}

Answer:

Option B:

\frac{1+xy}{3-x}

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