Question

X^2/x^2-3xy:x/x^2-9y^2

Answer 1

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Answer 2

To simplify the expression (x^2)/(x^2 - 3xy) : (x)/(x^2 - 9y^2), we can follow these steps:

Step 1: Factorize the denominators. The expression can be written as follows:

(x^2)/[x(x - 3y)] : (x)/[x(x + 3y)][x(x - 3y)]

Step 2: Cancel out common factors. We can cancel out common factors between the numerator and denominator. In this case, we can cancel out the factor of x in both terms:

(x^2)/(x^2 - 3xy) : (x)/(x^2 - 9y^2) = [x^2/(x^2 - 3xy)] * [(x^2 - 9y^2)/x]

Step 3: Simplify the expression. We have:

[x^2/(x^2 - 3xy)] * [(x^2 - 9y^2)/x] = [x^2(x^2 - 9y^2)] / [x(x^2 - 3xy)]

Now, we can further simplify the expression by canceling out the common factor of x:

= (x^2 - 9y^2) / (x - 3y)

Therefore, the simplified form of the expression (x^2)/(x^2 - 3xy) : (x)/(x^2 - 9y^2) is (x^2 - 9y^2) / (x - 3y).