Question

Please solve the questions 19,20 and 21.

Answer 1

19)question:
5/(x-2)-3/(x+6)=4/x
(5x+30-3x+6)/(x^2+6x-2x-12)=4/x
(2x+36)/(x^2+4x-12)=4/x
2x^2+36x=4x^2+16x-48
x^2-10x-24=0
x^2-12x+2x-24=0
(x+2)(x-12)=0
x=-2 and x=12

20)question
{1+1/(x+1)}{1-1/(x-1)}=7/8
{(x+1+1)/(x+1)}{(x-1-1)/(x-1)}=7/8
{(x+2)/(x+1)}{(x-2)/(x-1)}=7/8
(x^2-4)/(x^2-1)=7/8
8x^2-32=7x^2-7
x^2-25=0
(x-5)(x+5)=0
x=5 and x=-5

21)question
we know that any quadratic polynomial is in the form of,
I)
={x^2-(sum of the zeroes)x+ ( product of zeroes)}
={x^2-(3+5)x+(3×5)}
={x^2-8x+15}
This the required quadratic equation with solution (3,5)
ii)
={x^2-(-2+3)x+(-2×3)}
={x^2-x-6}
=x^2-x-6
This the required quadratic equation with solution. (-2,3).