What is 1/(3x-2y)+(x-y)/(9x^2-4y^2) ?

The solution to 1/(3x-2y)+(x-y)/(9x^2-4y^2) is (4x+y)/(9x^2-4y^2)

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simplify 1/(3x-2y)+(x-y)/(9x^2-4y^2)

simplify

\frac{1}{3 x - 2 y} + \frac{x - y}{9 x ^{2} - 4 y ^{2}}

\frac{4 x + y}{9 x ^{2} - 4 y ^{2}}

Solution steps

\frac{1}{3 x - 2 y} + \frac{x - y}{9 x ^{2} - 4 y ^{2}}

Least Common Multiplier of

3 x - 2 y, 9 x^{2} - 4 y^{2} : (3 x - 2 y) (9 x^{2} - 4 y^{2})

Adjust Fractions based on the LCM

= \frac{9 x ^{2} - 4 y ^{2}}{( 3 x - 2 y ) ( 9 x ^{2} - 4 y ^{2} )} + \frac{( x - y ) ( 3 x - 2 y )}{( 3 x - 2 y ) ( 9 x ^{2} - 4 y ^{2} )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{9 x ^{2} - 4 y ^{2} + ( x - y ) ( 3 x - 2 y )}{( 3 x - 2 y ) ( 9 x ^{2} - 4 y ^{2} )}

Simplify

9 x^{2} - 4 y^{2} + (x - y) (3 x - 2 y) : 12 x^{2} - 2 y^{2} - 5 x y

= \frac{12 x ^{2} - 2 y ^{2} - 5 x y}{( 3 x - 2 y ) ( 9 x ^{2} - 4 y ^{2} )}

Cancel

\frac{12 x ^{2} - 2 y ^{2} - 5 x y}{( 3 x - 2 y ) ( 9 x ^{2} - 4 y ^{2} )} : \frac{4 x + y}{9 x ^{2} - 4 y ^{2}}

= \frac{4 x + y}{9 x ^{2} - 4 y ^{2}}

\frac{cos ^{2} ( θ )}{1 - sin ( θ )} - 1

π - 2 π

3 \times (- 8)

(4 x + 3 y)^{2} - (2 x - 5 y)^{2}

(\frac{- 5 d}{c}) (\frac{c}{d})^{3}

What is 1/(3x-2y)+(x-y)/(9x^2-4y^2) ?
The solution to 1/(3x-2y)+(x-y)/(9x^2-4y^2) is (4x+y)/(9x^2-4y^2)