Bài : Thực hiện phép tính
a) 12x ³ – 28x ² + 21x – 5) : (6x – 5) – (2x ² – 4x)
b) ($\frac{x+1}{x-3}$ + $\frac{5x-39}{x^2-9}$ – $\frac{11}{x+3}$) : $\frac{x^2+2x+1}{2x+6}$
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Bài : Thực hiện phép tính a) 12x ³ – 28x ² + 21x – 5) : (6x – 5) – (2x ² – 4x) b) ($\frac{x+1}{x-3}$ + $\frac{5x-39}{x^2-9}$ – $\frac{11}{x+3}$) :
By Athena
Đáp án:
Giải thích các bước giải:
a) ta có (2x-1)(x-1)(6x-5):(6x-5)-2x(x-2)
=(2x-1)(x-1)-2x(x-2)
=2x^2-3x+1-2x^2+4x
=x+1
b ta có
($\frac{x+1}{x-3}$ +$\frac{5x-39}{x^2-9}$ -$\frac{11}{x+3}$ ):$\frac{x^2 +2x+1}{2x+6}$
=($\frac{(x+1).(x+3)}{(x-3).(x+3}$ +$\frac{5x-39}{(x-3)(x+3)}$ -$\frac{11.(x-3)}{x+3)(x-3)}$:$\frac{(x+1)^2}{2(x+3)}$
=$\frac{(x+1).(x+3)+(5x-39)-11.(x-3)}{(x-3)(x+3)}$ .$\frac{2(x+3)}{(x+1)^2}$
=$\frac{x^2+4x+3+5x-39-11x+33}{(x-3)(x+3)}$ .$\frac{2.(x+3)}{(x+1)^2}$
=$\frac{x^2-2x-3}{(x-3)(x+3)}$ .$\frac{2.(x+3)}{(x+1)^2}$
=$\frac{(x-3)(x+1)}{(x-3)(x+3)}$ .$\frac{2.(x+3)}{(x+1)^2}$
=$\frac{2}{x+1}$
Đáp án: `a) x+1`
`b)“ (2)/(x+1)`
Giải thích các bước giải:
`a)(12x ³ – 28x ² + 21x – 5) : (6x – 5) – (2x ² – 4x)`
`=(12x ³ – 18x ²-10x^2 + 6x + 15x – 5) : (6x – 5) – (2x ² – 4x)`
`=[(12x ³ – 18x ²+ 6x)+(-10x^2 + 15x – 5)] : (6x – 5) – (2x ² – 4x)`
`=[6x.(2x^2-3x+1)-5.(2x^2-3x+1) ] : (6x – 5) – (2x ² – 4x)`
`=[(6x-5).(2x^2-3x+1)] : (6x – 5) – (2x ² – 4x)`
`=(2x^2-3x+1) – (2x ² – 4x)=2x^2-3x+1-2x ² + 4x=x+1`
.
`b)“((x+1)/(x-3)+(5x-39)/(x^2-9)-(11)/(x+3)):(x^2+2x+1)/(2x+6)`
`=(((x+1)(x+3))/((x-3)(x+3))+(5x-39)/((x-3)(x+3))-(11.(x-3))/((x-3)(x+3))):(x+1)^2/(2(x+3))`
`=((x+1)(x+3)+5x-39-11.(x-3))/((x-3)(x+3)):(x+1)^2/(2(x+3))`
`=(x^2+4x+3+5x-39-11x+33)/((x-3)(x+3)):(x+1)^2/(2(x+3))`
`=(x^2-2x-3)/((x-3)(x+3)):(x+1)^2/(2(x+3))=((x-3)(x+1))/((x-3)(x+3)).(2(x+3))/(x+1)^2`
`=(x+1)/(x+3).(2(x+3))/((x+1)(x+1))=(2)/(x+1)`