(n)(1)/(x-3)-(1)/(x+5)=(1)/(6)(x!=3-5)

solve for x,(1)/(x-3)-(1)/(x+5)=(1)/(6)

Solve: (1)/(x-3)+(1)/(x+5)=(1)/(6) .

((1)/(x-3)-(3)/(x(x^(2)-5x+6)))

Add :5x^(2)-(1)/(3)x+(5)/(2),-(1)/(2)x^(2)+(1)/(2)x-(1)/(3) and -2x^(2)+(1)/(5)x-(1)/(6)

(x-1)/(3)+(2x+5)/(6)=(3x-6)/(9)-(2x-5)/(2)

Add: (3x^(2) - (1)/(5)x + (7)/(3)) + ((-1)/(4)x^(2) + (1)/(3)x - (1)/(6)) + (-2x^(2) - (1)/(2)x + 5)

Take away: (6)/(5)x^(2)-(4)/(5)x^(3)+(5)/(6)+(3)/(2)x om (x^(3))/(3)-(5)/(2)x^(2)+(3)/(5)x+(1)/(4)

3((7x+1)/(5x-3))-4((5x-3)/(7x+1))=11;x!=(3)/(5),-(1)/(7)

Assertion (A) : (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+…(1)/(2)log((3)/(2)) Reason (R ) : If |x| lt 1 then log_(e )((1+x)/(1-x))=2(x+(x^(3))/(3)+(x^(5))/(5)+…)

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sum of different series. Q. Sum of infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(2)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+ . . .oo is