Question

[Sara]

1. Tính

\(P=\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}+\frac{1}{x^2+11x+30}\)

Answer 1

[Khánh Hà]

\(P=\frac{1}{x^2+2x+3x+6}+\frac{1}{x^2+3x+4x+12}+\frac{1}{x^2+4x+5x+20}+\frac{1}{x^2+5x+6x+30^{ }}\)

\(P=\frac{1}{\left(x^2+2x\right)+\left(3x+6\right)}+\frac{1}{\left(x^2+3x\right)+\left(4x+12\right)}+\frac{1}{\left(x^2+4x\right)+\left(5x+20\right)}+\frac{1}{\left(x^2+5x\right)+\left(6x+30\right)}\)

\(P=\frac{1}{x\left(x+2\right)+3\left(x+2\right)}+\frac{1}{x\left(x+3\right)+4\left(x+3\right)}+\frac{1}{x\left(x+4\right)+5\left(x+4\right)}+\frac{1}{x\left(x+5\right)+6\left(x+5\right)}\)

\(P=\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}\)

\(P=\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}\)

\(P=\frac{1}{x+2}-\frac{1}{x+6}\)

\(P=\frac{x+6}{\left(x+2\right)\left(x+6\right)}-\frac{x+2}{\left(x+2\right)\left(x+6\right)}\)

\(P=\frac{x+6-x+2}{\left(x+2\right)\left(x+6\right)}\)

\(P=\frac{4}{\left(x+2\right)\left(x+6\right)}\)

Chúc cậu học tốt nha !

Answer 2

[Phạm Ngọc Linh]

P= 1/ x²+5x+6 + 1/ x²+ 7x+12 + 1/x²+9x+20 +1/ x²+11x+30
P=1/ x²+2x+3x+6 + 1/ x²+3x+4x+12 + 1/ x ²+4x+5x+20 + 1/ x²+6x+5x+30

P=1/x.(x+2) + 3.(x+2) + 1/ x.(x+3)+4.(x+3) + 1/ x.(x+4) + 5.(x+4) + 1/ x.(x+6)+5.(x +6)
P= 1/ (x+2).(x+3) + 1/(x+3).(x+4)+1/ ( x+4).(x+5)+1/(x+6).(x+5)
P=1.(x+4)(x+5)(x+6) /(x+2)(x+3)(x+4).(x+5)(x+6) + 1.(x+2)(x+5)(x+6)/ ( x+2)(x+3)(x+4)(x+5)(x+6) + 1(x+2)(x+3)(x+6)/ (x+2)(x+3)(x+4)(x+5)(x+6) +1.(x+2)(x+3)(x+4)/(x+2)(x+3)(x+4)(x+5)(x+6)
P = (x+4)(x+5)(x+6)+(x+2)(x+5)(x+6)+(X+2)(x+3)(x+6)+(x+2)(x+3)(x+4)/(x+2)(x+3)(x+4)(x+5)(x+6)

P=4/(x+2)(x+6)