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\(\frac{x^2-36}{2x+10}.\frac{3}{6-x}\)
\(=\frac{\left(x^2-36\right).3}{\left(2x+10\right)\left(6-x\right)}\)
\(=\frac{3\left(x+6\right)\left(x-6\right)}{\left(2x+10\right)\left(6-x\right)}\)
\(=-\frac{3\left(x+6\right)\left(x-6\right)}{2\left(x+5\right)\left(x-6\right)}\)
\(=-\frac{3\left(x+6\right)}{2\left(x+5\right)}\)
a) \(\left(2x-5\right)^2-\left(2x+3\right)\left(2x-3\right)=10\Leftrightarrow\left(4x^2-20x+25\right)-\left(4x^2-9\right)-10=0\)
\(\Leftrightarrow-20x+24=0\Leftrightarrow x=\frac{6}{5}\)
b) \(\left(4x-1\right)\left(x+2\right)-\left(2x+3\right)^2-5\left(x-1\right)=9\Leftrightarrow-10x-15=0\)
\(\Leftrightarrow x=\frac{-3}{2}\)
c) \(\left(x+1\right)^3-\left(x-1\right)^3-2=6\Leftrightarrow\left(x^3+3x^2+3x+1\right)-\left(x^3-3x^2+3x-1\right)-8=0\)
\(\Leftrightarrow6x^2-6=0\Leftrightarrow x=\pm1\)
d) \(\left(x+2\right)\left(x^2-2x+4\right)-\left(x+1\right)\left(x^2-x+1\right)-3\left(-x-2\right)=5\)
\(\Leftrightarrow\left(x^3+8\right)-\left(x^3+1\right)+3x+6=5\Leftrightarrow3x+8=0\Leftrightarrow x=\frac{-8}{3}\)
a)(x+2).(x+3)-(x-2).(x+5)=10
( x^2 +3x+2x+6)-(x^2 +5x-2x-10)=10
x^2 +3x+2x+6-x^2 -5x+2x+10-10=0
2x+6=0
2x=-6
x=-3
a)\(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6.\)
\(\Leftrightarrow x^2-4x+4-x^2+9-6=0\)
\(\Leftrightarrow-4x+7=0\)
\(\Leftrightarrow4x=7\Leftrightarrow x=1,75\)
\(b,4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10.\)
\(\Leftrightarrow4\left(x^2-6x+9\right)-4x^2+1-10=0\)
\(\Leftrightarrow-24x+27=0\)
\(\Leftrightarrow24x=27\Leftrightarrow x=1,125\)
a)
<=> 10x - 35 + 16x - 10 = 5
<=> 10x + 16x = 5 + 35 + 10
<=> 26x = 50
<=> x = 50/26 = 25/13
a ) \(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\)
\(\Leftrightarrow x^2-4x+4-x^2+9=6\)
\(\Leftrightarrow-4x+13=6\)
\(\Leftrightarrow-4x=-7\)
\(\Leftrightarrow x=\frac{7}{4}\)
Vậy \(x=1\).
b ) \(4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
\(\Leftrightarrow4\left(x^2-6x+9\right)-\left(4x^2-1\right)=10\)
\(\Leftrightarrow4x^2-24x+36-4x^2+1=10\)
\(\Leftrightarrow-24x+37=10\)
\(\Leftrightarrow-24x=27\)
\(\Leftrightarrow x=\frac{9}{8}.\)
Mấy pài kia tương tự . :D
a, (x-2)^2 - (x-3)(x+3)=6
x^2-4x+4-(x^2-9)=6
x^2-4x+4-x^2+9=6
(x^2-x^2)-4x+13=6
-4x=-7
x=1,75
b, 4(x-3)^2 - (2x-1)(2x+1)=10
4(x^2-6x+9)-(4x^2-1)=10
4x^2-24x+36-4x^2+1=10
-24x+37=10
x=9/8
c,(x-4)^2 - (x+2)(x-2)=6
x^2-8x+16-(x^2-4)=6
x^2-8x+16-x^2+4=6
-8x+20=6
x=7/4
d, 9(x+1)^2 - (3x-2)(3x+2)=10
9(x^2+2x+1)-(9x^2-4)=10
9x^2+18x+9-9x^2+4=10
18x+13=10
x=-1/6
\(a,\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\)
\(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\)
\(-4x+13=6\)
\(-4x=6-13\)
\(-4x=-7\)
\(x=\frac{-7}{-4}\)
\(x=\frac{7}{4}\)
Vậy \(x=\frac{7}{4}\)
\(b,4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
\(4\left(x^2-6x+9\right)-\left(4x^2-1\right)=10\)
\(4x^2-24x+36-4x^2+1=10\)
\(-24x+37=10\)
\(x=\frac{9}{8}\)
Vậy \(x=\frac{9}{8}\)
\(c,\left(x-4\right)^2-\left(x+2\right)\left(x-2\right)=6\)
\(x^2-8x+16-\left(x^2-4\right)=6\)
\(x^2-8x+16-x^2+4=6\)
\(-8x+20=6\)
\(x=\frac{7}{4}\)
Vậy \(x=\frac{7}{4}\)
\(d,9\left(x+1\right)^2-\left(3x-2\right)\left(3x+2\right)=10\)
\(9\left(x^2+2x+1\right)-\left(9x^2-4\right)=10\)
\(9x^2+18x+9-9x^2+4=10\)
\(18x+13=10\)
\(x=\frac{-1}{6}\)
Vậy \(x=\frac{-1}{6}\)
Bài 1.
a) ( x - 2)2 - ( x + 3)( x - 3)= 17
=> x2 - 4x + 4 - x2 + 9 - 17 = 0
=> -4x - 4 = 0
=> -4( x + 1 ) = 0
=> x = -1
Vậy,...
b)4( x - 3)2 - ( 2x - 1)( 2x + 1) = 10
=> 4( x2 - 6x + 9) - 4x2 + 1 - 10 = 0
=> - 24x + 36 - 9 = 0
=> -24x + 27 = 0
=> -3( 8x - 9) = 0
=> x = \(\dfrac{9}{8}\)
Vậy,...
c) ( x - 4)2 - ( x - 2)( x + 2)= 36
=> x2 - 8x + 16 - x2 + 4 - 36 = 0
=> -8x - 16 = 0
=> -8( x + 2) = 0
=> x = -2
d) ( 2x + 3)2 - ( 2x + 1)( 2x - 1) = 10
=> 4x2 + 12x + 9 - 4x2 + 1 - 10 = 0
=> 12x = 0
=> x = 0
Vậy,...
Bài 2.
\(\dfrac{3x^2+3x}{\left(x+1\right)\left(2x-6\right)}\)
a) ĐKXĐ : ( x + 1)( 2x - 6) # 0
=> 2( x + 1)( x - 3) # 0
=> x # -1 ; x # 3
Vậy,...
b) Để P = 1
=> \(\dfrac{3x^2+3x}{\left(x+1\right)\left(2x-6\right)}=1\)
=> \(\dfrac{3x\left(x+1\right)}{2\left(x+1\right)\left(x-3\right)}=\dfrac{3x}{2\left(x-3\right)}=1\)
=> 3x = 2x - 6
=> x = -6 ( thỏa mãn ĐKXĐ)
Vậy,...
Bài 3.
P = \(\dfrac{x}{x-1}+\dfrac{x^2+1}{1-x^2}\)
a) Để P có nghĩa tức P xác định .
ĐKXĐ : x - 1 # 0 => x # 1
* 1 - x2 # 0 => x # 1 ; x # -1
Vậy,...
b) P = \(\dfrac{x}{x-1}+\dfrac{x^2+1}{1-x^2}\)
P = \(\dfrac{x^2+x-x^2-1}{\left(x-1\right)\left(x+1\right)}=\dfrac{x-1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x+1}\)( x# 1; x# -1)
c) Để P = -1 thì :
\(\dfrac{1}{x+1}=-1\)
=> -x - 1 = 1
=> x = -2 ( thỏa mãn ĐKXĐ )
Vậy,...
a) (x - 2)2 - (x - 3)(x + 3) = 17
⇔ (x2 - 4x + 4) - (x2 - 9) = 17
⇔ x2 - 4x + 4 - x2 + 9 = 17
⇔ 13 - 4x = 17
⇔ - 4x = -4
⇔ x = 1
b) 4(x - 3)2 - (2x - 1)(2x + 1) = 10
⇔ [2(x - 3)]2 - (4x2 - 1) = 10
⇔ (2x - 6)2 - 4x2 + 1 = 10
⇔ 4x2 - 24x + 36 - 4x2 + 1 = 10
⇔ - 24x = -27
⇔ x = \(\dfrac{9}{8}\)
c) (x - 4)2 - (x - 2)(x + 2) = 36
⇔ x2 - 8x + 16 - x2 + 4 = 36
⇔ -8x = 16
⇔ x = -2
d) (2x + 3)2 - (2x - 1)(2x + 1) = 10
⇔ 4x2 + 12x + 9 - 4x2 + 1 = 10
⇔ 12x = 0
⇔ x = 0
Tìm x ,biết :
a, \(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=17\)
\(\Rightarrow x^2-4x+4-x^2+9=17\)
\(\Rightarrow-4x+13=17\)
\(\Rightarrow-4x=4\)
\(\Rightarrow x=-1\)
b,\(4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
\(\Rightarrow4\left(x^2-6x+9\right)-4x^2+1=10\)
\(\Rightarrow4x^2-24x+36-4x^2+1=10\)
⇒ \(-24x+37=10\)
\(\Rightarrow-24x=-27\)
\(\Rightarrow x=\dfrac{-27}{-24}=\dfrac{9}{8}\)
c,\(\left(x-4\right)^2-\left(x-2\right)\left(x+2\right)=36\)
⇒ \(x^2-8x+16-x^2+4=36\)
⇒ \(-8x+20=36\)
⇒ \(-8x=16\Rightarrow x=-2\)
d,\(\left(2x+3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
\(\Rightarrow4x^2+12x+9-4x^2+1=10\)
\(\Rightarrow12x+10=10\)
\(\Rightarrow12x=0\Rightarrow x=0\)