What is (x^2+2x+1)/(x^2+5x+4) ?

The solution to (x^2+2x+1)/(x^2+5x+4) is (x+1)/(x+4)

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simplify (x^2+2x+1)/(x^2+5x+4)

simplify

\frac{x ^{2} + 2 x + 1}{x ^{2} + 5 x + 4}

\frac{x + 1}{x + 4}

Solution steps

\frac{x ^{2} + 2 x + 1}{x ^{2} + 5 x + 4}

Factor

x^{2} + 2 x + 1 : (x + 1)^{2}

= \frac{( x + 1 ) ^{2}}{x ^{2} + 5 x + 4}

Factor

x^{2} + 5 x + 4 : (x + 1) (x + 4)

= \frac{( x + 1 ) ^{2}}{( x + 1 ) ( x + 4 )}

Apply exponent rule:

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

(x + 1)^{2} = (x + 1) (x + 1)

= \frac{( x + 1 ) ( x + 1 )}{( x + 1 ) ( x + 4 )}

Cancel the common factor:

x + 1

= \frac{x + 1}{x + 4}

[4 + {(2 - 5)^{2} - 4 (7 - 5)^{3} + 2 (\frac{15}{3})}] - 16

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

(2 x - 6)^{2}

x \cdot (- x)

2 (x - 1)

What is (x^2+2x+1)/(x^2+5x+4) ?
The solution to (x^2+2x+1)/(x^2+5x+4) is (x+1)/(x+4)