Question

Please help...*puppy eyes* (Will pick brainliest)

Answer 1

Step-by-step explanation:

Note that the denominators in the expression are perfect squares:

${x}^{2} - 5xy + 6 {y}^{2} = (x - 2y)(x - 3y)$

${x}^{2} - 4xy + 3 {y}^{2} = (x - y)(x - 3y)$

${x}^{2} - 3xy + 2 {y}^{2} = (x - y)(x - 2y)$

We can then write the given expression as

$\frac{1}{ {x}^{2} - 5xy + 6 {y}^{2} } + \frac{a}{{x}^{2} - 4xy + 3{y}^{2} } + \frac{1}{{x}^{2} - 3xy + 2{y}^{2}}$

$\frac{1}{ {x}^{2} - 5xy + 6 {y}^{2} } + \frac{a}{{x}^{2} - 4xy + 3{y}^{2} } + \frac{1}{{x}^{2} - 3xy + 2{y}^{2}}$

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

$= \frac{(x - y)(x - 2y) {(x -3y)}^{2} + a {(x - y)}^{2} (x - 2y)(x - 3y) + (x - y){(x - 2y)}^{2}(x - 3y) }{ {(x - y)}^{2} {(x - 2y)}^{2} {(x - 3y)}^{2} }$