`(5x)/(3)-(x-2)/(3)=(9)/(4)-(1)/(2)(x-(2x-1)/(3))`

(x-1)/(3)+(2x+5)/(6)=(3x-6)/(9)-(2x-5)/(2)

Simplify :((-3)/(2)x(4)/(5))+((9)/(5)x(-10)/(3))-((1)/(2)x(3)/(4))

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

Check whether the following are quadratic equations : (1) (x-3)^(2)=x(2x-5) (2) (2x-3)(8x+1) = (4x+5)(4x-5) (3) (5x+3)(x-2)=(4x+3)(2x-1) (4) (2x+5)^(3)=8(x-1)^(3) (5) x^(2)+7x-8=x(x+5) (6) x^(3)+9x^(2)-7x+2=(x+3)^(3)

Simplify: ((1)/(4)x(2)/(7))-((5)/(14)x(-2)/(3))+((3)/(7)x(9)/(2))

((x+1)-(2x+4))/(3-5x)=(1)/(23)

If 5(tan^(2)x-cos^(2)x)=2cos2x+9, then the value of cos4x is: (2)/(9)(2)-(7)/(9)(3)-(3)/(5)(4)(1)/(3)

3x-(5x^(2))/(2)+(9x^(3))/(3)-(17x^(4))/(4)+....+(-1)^(n-1)((2^(n)+1))/(2)x^(n)+...=

Observe the following pattern (1x2)+(2x3)=(2x3x4)/(3)(1x2)+(2x3)+(3x4)=(3x4x5)/(3)(1x2)+(2x3)+(3x4)+(4x5)=(4x5x6)/(3) and find the of (1x2)+(2x3)+(3x4)+(4x5)+(5x6)

Check whether the following are quadratic equations : (1) (x-1)^(2)=2(x-3) (2) x^(2)-2x=(-2)(3-x) (3) (x-2)(x+1)=(x-1)(x+3) (4) (x-3)(2x+1)=x(x+5) (5) (2x-1)(x-3)=(x+5)(x-1) (6) x^(2)+3x+1=(x-2)^(2) (7) (x+2)^(3)=2x(x^(2)-1) (8) x^(3)-4x^(2)-x+1=(x-2)^(3)