Solution (1-1/(x-1))/(x/(x-1))
=((x-2)/(x- 1))/(x/(x+ 1)(x- 1))
=(x-2)/(x- 1)*(x+ 1)(x- 1)/x
=(x-2)(x+ 1)/x
When x=2, the original formula =0.
The appropriate value of x must not be 1,-1, 0.
2. 1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y), where x-y = 6 and xy = 2 1.
Simplify:
1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y) =1
1/2[(x+y) square +2z(x+y)+z square ]+ 1/2[(x-y) square -z square ]-z(x+y)=]
1/2(x+y) square+1/2(x-y) square =x square +y square.
From x-y=6, xy=2 1, x+y = (x-y)+2xy = 78.
3.9x+6x2-3 (x-2/3x2), where x=-2.
9x+6x？ -3(x-2/3x？ )
=9x+6x？ -3x+2x？
=8x？ +6 times
=8×(-2)? +6×(-2)
=32- 12
=20
4.9x+6x2-3 (x-2/3x2), where x=-2.
9x+6x？ -3(x-2/3x？ )
=9x+6x？ -3x+2x？
=8x？ +6 times
=8×(-2)? +6×(-2)
=32- 12
=20
5.1/4 (-4x2+2x-8)-(1/2x-1), where x= 1/2.
1/4(-4x？ +2x-8)-( 1/2x- 1)
=-x？ + 1/2x-2- 1/2x+ 1
=-x？ - 1
=-( 1/2)? - 1
=- 1/4- 1
=-5/4
6.3x' y-[2x' y-(2xyz-x' z)-4x' z]-XYZ, where x =-2, y =-3, z = 1,
:3x ' y-[2x ' y-(2xyz-x ' z)-4x ' z]-XYZ
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
=4*(-3)-2*3* 1+3*4* 1
=- 12-6+ 12
=-6
7.(5a 2-3b 2)+(a 2+b 2)-(5a 2+3b 2), where a =- 1 and b = 1.
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(- 1)^2-5* 1^2
= 1-5
=-4
8.2 (A2B+AB 2)-2 (A2B-1)-2AB 2-2, where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
9. Square of (x-21y-1) (x-21y+1)-(x-21y-1)
Where x = 1.7 and y = 3.9 (simplify first and then evaluate).
[(X-2 is 1Y)- 1][(X+2 is 1Y)+ 1]-(X-2 is1y-0/) square.
= (x+ 1Y) square-1-(x- 1Y) square +2 (x- 1Y)- 1.
= (x+ 1Y) square -(x- 1Y) square +2 (x- 1y) -(X-2
=2XY+2X-Y-2
=3.9*2.4+ 1.4
= 10.76
10. Simplify before evaluating.1/2a-(2a-2/3b2)+(-3/2a+2b2) where a =-2 and b = 2/3.
Original formula =-3a+8/3b 2
When a=-2 and b=2/3,
The original formula =6+8/3×(4/9)= 194/27.