Question

What is the simplified form of the quantity x squared minus 5x plus 6 over 15 x y squared all over the quantity 2x squared minus 7x plus 3 over 5 x squared y ?

a.3y times the quantity 2x plus 1 over x times the quantity x plus 2

b.x times the quantity x plus 2 over 3y times the quantity 2x plus 1

c.x times the quantity x minus 2 over 3y times the quantity 2x minus 1

d.3y times the quantity 2x minus 1 over x times the quantity x minus 2

Answer 1

`(x^(2) - 5x + 6)/(15xy^(2)) / (2x^(2) - 7x + 3)/(5x^(2)y)`

`(x^(2) - 5x + 6)/(15xy^(2)) * (5x^(2)y)/(2x^(2) - 7x + 3)`

`((x - 3)(x - 2))/(3y) * (x)/((2x - 1)(x - 3))`

`(x - 2)/(3y) * (x)/(2x - 1)`

`(x^(2) - 2x)/(6xy - 3y)`

The answer is C.

Answer 2

C is the correct option.

Explanation:

We have been given the expression

When we flip the denominator, the division sign gets changed to multiplication. The rule is shown below

`((a)/(b))/((c)/(d))=(a)/(b)*(d)/(c)`

Using this rule, we have

`(x^2-5x+6)/(15xy^2)*(5x^2y)/(2x^2-7x+3)`

Now, we can factor the quadratic expressions as

`x^2-5x+6=x^2-3x-2x+6=(x-3)(x-2)`

`2x^2-7x+3=2x^2-6x-x=(x-3)(2x-1)`

On plugging these values, we get

`((x-3)(x-2))/(3\cdot5\cdot xy^2)*(5x^2y)/((x-3)(2x-1))`

On cancelling the common terms in numerator and denominator, we get

`(x(x-2))/(3y(2x-1))`

Hence, C is the correct option.