If `A=(x)/(x+1), B=(1)/(x+1), prove that `((A+B)^(2)+(A-B)^(2))/(A÷B)=(2(x^(2)+1))/(x(x+1)^(2))`

If A=(2x+1)/(2x-1), B=(2x-1)/(2x+1) find (1)/(A-B)-(2B)/(A^(2)-B^(2))

If a+ib = (x+i)^(2)/(2x^(2)+1) , prove that a^(2) + b^(2) = (x^(2)+1)^(2)/(2x^(2) + 1)^(2)

If (x+a) (x+b) (x+c) =x^(3) +14x^(2) +59x + 70 , find the value of (i) a+b+c (ii) (1)/(a) +(1)/(b) +(1)/(C ) ( iii) a^(2) +b^(2) +c^(2) (iv) (a)/(bc) +(b)/( ac) +(c )/( ab)

If (x+1/x+1)^(6)=a_(0)+(a_(1)x+(b_(i))/(x))+(a_(2)x^(2)+(b_(2))/(x^(2)))+"...."+(a_(6)x^(6)+(b_(6))/(x^(6))) , then

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

Consider the polynomial fucntion f(x) = |{:((1+x)^(2),,(1+2x)^(b),,1),(1,,(1+x)^(a),,(1+2x)^(b)),((1+2x)^(b),,1,,(1+x)^(a)):}| a,b being positive integers. the coefficient of x in f(x) is