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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= \frac{( 2 x + y ) ( 2 x + y )}{( 2 x + y ) ( 2 x - y )}

Cancel the common factor:

2 x + y

= \frac{2 x + y}{2 x - y}

5 (p - 7) - 2 (3 p - 4) = 3 p

n^{2} - 14 n + 40

\frac{3}{2 - 5}

\frac{x ^{- 3} y ^{0} \cdot ( x y ^{- 3} ) ^{2}}{2 x ^{0}}

4 (x + 6) = 36

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