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

Answer:

C is the correct option.

Step-by-step explanation:

We have been given the expression

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

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Using this rule, we have

$\frac{x^2-5x+6}{15xy^2}\times\frac{5x^2y}{2x^2-7x+3}$

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

$\frac{(x-3)(x-2)}{3\cdot5\cdot xy^2}\times\frac{5x^2y}{(x-3)(2x-1)}$

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

$\frac{x(x-2)}{3y(2x-1)}$

Hence, C is the correct option.

Answer 2

$\frac{x^{2} - 5x + 6}{15xy^{2}} \div \frac{2x^{2} - 7x + 3}{5x^{2}y}$
$\frac{x^{2} - 5x + 6}{15xy^{2}} \times \frac{5x^{2}y}{2x^{2} - 7x + 3}$
$\frac{(x - 3)(x - 2)}{3y} \times \frac{x}{(2x - 1)(x - 3)}$
$\frac{x - 2}{3y} \times \frac{x}{2x - 1}$
$\frac{x^{2} - 2x}{6xy - 3y}$

The answer is C.