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

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)

Simplify the following:(x-2y) (y-3x)+(x+y) (x-3y)- (y-3x)(4x-5y).

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

1/(3x+y)+1/(3x-y)=3/4 and 1/(3x+y)-1/(3x-y)= -1/4

Find (x+y)+(x-y), if x=(5)/(4),y=(-1)/(3) (ii) x=(2)/(7),y=(4)/(3)( iii) x=(1)/(4),y=(3)/(2)

{:((1)/(2(x + 2y)) + (5)/(3(3x - 2y))=(-3)/(2)),((5)/(4(x + 2y)) - (3)/(5(3x - 2y)) = (61)/(60)):}

Solve the simultaneous equations : 10/(x+y) + 2/(x-y) = 4, 5/(x+y) -5/(3(x-y)) = (-2)/3

Find the following products and verify the result for x=-1,y=-2:(3x-5y)(x+y)(2)(x^(2)y-1)(3-2x^(2)y)((1)/(3)x-(y^(2))/(5))((1)/(3)x+(y^(2))/(5))

The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y-3=0 and 2x-y+4=0 , and their respective lengths are sqrt(2) and 2sqrt(3)dot The equation of the hyperbola is 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 2(2x-y+4)^2-3(x+2y-3)^2=1 2(x+2y-3)^2-3(2x-y+4)^2=1