`(1)(x+2)(x+3)(x-4)(x-5)=44`

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)

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

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)

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)

Solve : (i)" "((x-1)\(x-2)(x-3))/((x+1)(x+2)(x+3))" "(ii) " "(x^(4)+x^(2)+1)/(x^(2)+4x-5)lt0

Solve : (i)" "((x-1)\(x-2)(x-3))/((x+1)(x+2)(x+3))" "(ii) " "(x^(4)+x^(2)+1)/(x^(2)+4x-5)lt0

lim_(x rarr1)[(x+2)/(x^(2)-5x+4)+(x-4)/(3(x^(2)-3x+2))]