What is (x^2-4xy+3y^2)/(y^2-x^2) ?

The solution to (x^2-4xy+3y^2)/(y^2-x^2) is -(x-3y)/(y+x)

Popular >

simplify (x^2-4xy+3y^2)/(y^2-x^2)

simplify

\frac{x ^{2} - 4 x y + 3 y ^{2}}{y ^{2} - x ^{2}}

- \frac{x - 3 y}{y + x}

Solution steps

\frac{x ^{2} - 4 x y + 3 y ^{2}}{y ^{2} - x ^{2}}

Factor

x^{2} - 4 x y + 3 y^{2} : (x - y) (x - 3 y)

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

y^{2} - x^{2} = (y + x) (y - x)

= \frac{( x - y ) ( x - 3 y )}{( y + x ) ( y - x )}

(y + x) (y - x) = - (y + x) (x - y)

= \frac{( x - y ) ( x - 3 y )}{- ( y + x ) ( x - y )}

Cancel the common factor:

x - y

= \frac{x - 3 y}{- ( y + x )}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{x - 3 y}{y + x}

(\frac{x}{7} + \frac{y}{6})^{3}

\frac{x ^{2}}{y ^{2}} + \frac{y ^{2}}{x ^{2}}

x^{4} + x^{3} - 2

(x + x^{2} + x^{3})^{3}

\frac{v}{( x ^{2} \cdot y ^{3} )} + \frac{u}{x} - w

What is (x^2-4xy+3y^2)/(y^2-x^2) ?
The solution to (x^2-4xy+3y^2)/(y^2-x^2) is -(x-3y)/(y+x)