How to calculate 1 / 3x + 6 = 1 / 2 (x + 6)

How to calculate 1 / 3x + 6 = 1 / 2 (x + 6)

Multiply both sides by six
2x+36=3(x+6)
2x+36=3x+18
∴x=18

(x-1)/(x^2+3x+2)+6/(2+x-x^2)-(10-x)/(4-x^2)

The beauty of Mathematics
[+ 2] / (x) (1) / (x) (x)] (x)
= (x-1)(x-2) / [(x+1)(x+2)(x-2)] - 6(x+2)/ [ (x+1)(x-2)(x+2) ] - (x -10)(x+1) / [ (x+2)(x-2)(x+1) ]
= [ (x² - 3x+2) - (6x+12) - (x² - 9x - 10) ] / [ (x+2)(x-2)(x+1) ]
= 0
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(1) X ^ 2 + 3x + 2 of X-1 + 2 + x-x ^ 2 of 6-4-x ^ 2 of 10-x
(2) X-Y of X multiplied by X + y of Y ^ 2-x ^ 4-y ^ 4 of x ^ 4Y divided by x ^ 2 + y ^ 2 of x ^ 2
(3) When x = - 2, find x + 1 / 1-x ^ 2-1 / x + 3 divided by x ^ 2-2x + 1 / x ^ 2 + 4x + 3
Yes, I'll give you 100 points

X ^ 2 + 3x + 2 of X-1 + 2 + x-x ^ 2 of 6-4-x ^ 2 of 10-x
=(x-1)/(x²+3x+2)+6/(2+x-x²)-(10-x)/(4-x²)
=(x-1)/(x+1)(x+2)-6/(x-2)(x+1)-(x-10)/(x-2)(x+2)
=[(x-1)(x-2)-6(x+2)-(x-10)(x+1)]/(x+1)(x+2)(x-2)
=(x²-3x+2-6x-12-x²+9x+10)/(x+1)(x+2)(x-2)
=0/(x+1)(x+2)(x-2)
=0
(2) X-Y of X multiplied by X + y of Y ^ 2-x ^ 4-y ^ 4 of x ^ 4Y divided by x ^ 2 + y ^ 2 of x ^ 2
=x/(x-y)*y²/(x+y)*(x⁴y)/(x⁴-y⁴)÷x²/(x²+y²)
=x^5y³/[(x²-y²)(x²-y²)(x²+y²)]÷x²/(x²+y²)
=x³y³/(x²-y²)²
(3) When x = - 2, find x + 1 / 1-x ^ 2-1 / x + 3 divided by x ^ 2-2x + 1 / x ^ 2 + 4x + 3
X + 1 of 1-x ^ 2-1 of X + 3 divided by x ^ 2-2x + 1 of x ^ 2 + 4x + 3
=1/(x+1)-(x+3)/(x²-1)÷(x²+4x+3)/(x²-2x+1)
=1/(x+1)-(x+3)/(x-1)(x+1)÷(x+1)(x+3)/(x-1)²
=1/(x+1)-1/(x+1)²
=(x+1-1)/(x+1)²
=x/(x+1)²
=-2/(-2+1)²
=-2/1
=-2