rút gọn A
A=5X+3-|6X-4|
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\(5x+3-|6x-4|\)
\(=5x+3-6x-4\)
\(=\left(5x-6x\right)+\left(3+4\right)\)
\(=x+7\)
\(=\dfrac{\left(4x^2+6x\right)\left(6x+3\right)-5x-5}{\left(6x+3\right)\left(5x+5\right)}\)
\(=\dfrac{24x^3+12x^2+36x^2+18x-5x-5}{\left(6x+3\right)\left(5x+5\right)}\)
\(=\dfrac{24x^3+48x^2+13x-5}{\left(6x+3\right)\left(5x+5\right)}\)
1)
\(ĐKXĐ:x\ne-1\)
\(\dfrac{x^2+2x+1}{x+1}\\ =\dfrac{\left(x+1\right)^2}{x+1}\\ =x+1\)
2)
ĐKXĐ x khác 0 và x khác 3
\(\dfrac{x^2-6x+9}{x\left(x-3\right)}\\ =\dfrac{\left(x-3\right)^2}{x\left(x-3\right)}\\ =\dfrac{x-3}{x}\)
3)
ĐKXĐ: x khác 0 và x khác -2
\(\dfrac{x^2-4}{2x\left(x+2\right)}\\ =\dfrac{\left(x-2\right)\left(x+2\right)}{2x\left(x+2\right)}\\ =\dfrac{x-2}{2x}\)
4)
DKXĐ: x khác 0 và x khác 2
\(\dfrac{x^2-2x}{5x^2-10x}\\ =\dfrac{x\left(x-2\right)}{5x\left(x-2\right)}\\ =\dfrac{1}{5}\)
`1)` Biểu thức xác định `<=>x+1 \ne 0<=>x \ne -1`
`[x^2+2x+1]/[x+1]=[(x+1)^2]/[x+1]=x+1`
`2)` Bth xác định `<=>x(x-3) \ne 0<=>{(x \ne 0),(x \ne 3):}`
`[x^2-6x+9]/[x(x-3)]=[(x-3)^]/[x(x-3)]=[x-3]/x`
`3)` Bth xác định `<=>2x(x+2) \ne 0<=>{(x \ne 0),(x \ne -2):}`
`[x^2-4]/[2x(x+2)]=[(x-2)(x+2)]/[2x(x+2)]=[x-2]/[2x]`
`4)` Bth xác định `<=>5x^2-10x \ne 0<=>5x(x-2) \ne 0<=>{(x \ne 0),(x \ne 2):}`
`[x^2-2x]/[5x^2-10x]=[x(x-2)]/[5x(x-2)]=1/5`
a) \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(=36x^2+12x+1+36x^2-12x+1-72x^2+2\)
\(=4\)
c) \(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)
\(=2x^3-3x-5x^3-x^2+x^2\)
\(=-3x^3-3x\)
d) \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)
\(=3x^2-6x-5x+5x^2-8x^2+24\)
\(=-11x+24\)
a) (6x+1)2 + (6x-1)2 - 2(1+6x)(6x-1)
= (6x+1+6x-1)2
=144x2
b) x(2x2 -3) - x2(5x+1) +x2
=2x3 - 3x - 5x3 -x2+x2
=-3x3-3x
=-3x(x2+1)
c) 3(22+1)(24+1)(28+1)(216+1)
= (22-1)(22+1)(24+1)(28+1)(216+1)
= (24-1)(24+1)(28+1)(216+1)
= (28-1)(28+1)(216+1)
= (216-1)(216+1)
= 232 -1
d) 3x(x-2) - 5x(1-x) - 8(x2 -3)
= 3x2-6x - 5x + 5x2 - 8x2 +24
= -11x +24
\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(=\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)
\(=\left(6x+1-6x+1\right)^2\)
\(=4\)
\(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)
\(=2x^3-3x-5x^3-x^2+x^2\)
\(=\left(2x^3-5x^3\right)+\left(x^2-x^2\right)-3x\)
\(=-3x^3-3x\)
\(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)
\(=3x^2-6x-5x+5x^2-8x^2+24\)
\(=\left(3x^2+5x^2-8x^2\right)-\left(6x+5x\right)+24\)
\(=-11x+24\)