13. `(x-1)/(x^2+5x) - (x-1)/(x^2-25)` 14. `3/(x-y)+5/(y^2-x^2)`

(14)/(x+y)+(3)/(x-y)=5,(21)/(x+y)-(2)/(x-y)=1

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)

If y=tan^(-1)((4x)/(1+5x^(2)))+tan^(-1)((2+3x)/(3-2x)) , then (dy)/(dx) is equal to a) (5)/(1+25x^(2)) b) (1)/(1+25x^(2)) c)0 d) (5)/(1-25x^(2))

Write t for ture and f for false for each of the following: 1. In-x, the constant trem is -1 2. The coefficient of x in x^2-3x+5 is 3. (5x-7)-(3x-5)=2x-12 4. (3x+5y)(3x-5y)=(9x^2-25y^2) 5. If a=2 and b= 1/2 then value of ab(a^2+b^2) is 4.1/4

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))

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))

Simplify : (i) (5x - 9y) - (-7x + y) (ii) (x^(2) -x) -(1)/(2)(x - 3 + 3x^(2)) (iii) [7 - 2x + 5y - (x -y)]-(5x + 3y -7) (iv) ((1)/(3)y^(2) - (4)/(7)y + 5) - ((2)/(7)y - (2)/(3)y^(2) + 2) - ((1)/(7)y - 3 + 2y^(2))

If y = tan^(-1) ((1)/(1 + x + x^(2))) + tan^(-1) ((1) /(x^(2) + 2x + 3)) + tan^(-1) ((1)/(x^(2) + 5x + 7)) + ….n terms , then y(0) is

{:("Column" A ,, "Column" B), (225x^(2) - 625 y^(2) = ,, (a) 25(x-2) (x-2)), (x^(2) - x - y - y^(2) = ,, (b) 25(3x- 5y) (3x + 5y)), (x^(2) - x - y^(2) + y = ,, (x + y) (x - y- 1)), (25x^(2) - 100 x + 100 = ,, (d) (x - y) (x + y -1)), (,,(e) (x + y) (x + y - 1)):}