What is (b^2)/(4a^2-4ab+b^2)+(a-b)/(2a-b) ?

The solution to (b^2)/(4a^2-4ab+b^2)+(a-b)/(2a-b) is (-2b^3+4a^3+7b^2a-8ba^2)/((2a-b)(b^2-4ba+4a^2))

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simplify (b^2)/(4a^2-4ab+b^2)+(a-b)/(2a-b)

simplify

\frac{b ^{2}}{4 a ^{2} - 4 ab + b ^{2}} + \frac{a - b}{2 a - b}

\frac{- 2 b ^{3} + 4 a ^{3} + 7 b ^{2} a - 8 b a ^{2}}{( 2 a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )}

Solution steps

\frac{b ^{2}}{4 a ^{2} - 4 ab + b ^{2}} + \frac{a - b}{2 a - b}

Least Common Multiplier of

4 a^{2} - 4 ab + b^{2}, 2 a - b : (2 a - b) (b^{2} - 4 ba + 4 a^{2})

Adjust Fractions based on the LCM

= \frac{b ^{2} ( 2 a - b )}{( 2 a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )} + \frac{( a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )}{( 2 a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )}

Apply the fraction rule:

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

= \frac{b ^{2} ( 2 a - b ) + ( a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )}{( 2 a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )}

Simplify

b^{2} (2 a - b) + (a - b) (b^{2} - 4 ba + 4 a^{2}) : - 2 b^{3} + 4 a^{3} + 7 b^{2} a - 8 b a^{2}

= \frac{- 2 b ^{3} + 4 a ^{3} + 7 b ^{2} a - 8 b a ^{2}}{( 2 a - b ) ( b ^{2} - 4 ba + 4 a ^{2} )}

5 + 45

\frac{1}{3} + \frac{2}{9} + \frac{4}{27} + \frac{8}{81} + \frac{16}{243}

52 + 52

23 \cdot 33

\frac{18}{6}

What is (b^2)/(4a^2-4ab+b^2)+(a-b)/(2a-b) ?
The solution to (b^2)/(4a^2-4ab+b^2)+(a-b)/(2a-b) is (-2b^3+4a^3+7b^2a-8ba^2)/((2a-b)(b^2-4ba+4a^2))