If (`3x)/((x-a)(x-b))=(2)/(x-a)+(1)/(n-b)` then a:b

If (x^(2))/((x-a)(x-b))=1+(a^(2))/((a-b)(x-a))+(B)/((x-b)) , then B is _________.

The cofficient of x^(n) in (x)/((x-a)(x-b)) is (a^(n)-b^(n))/(a-b)xx(1)/(a^(n)b^(n))

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

Let a,b,c be such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x) then (a)/(1)+(b)/(3)+(c)/(5)

If a=x+(1)/(x),b=x-(1)/(x), then the value of a^(2)+2ab-3b^(2) is

When two ratios are equal, then the four quantities compositing them are said to be proportiona. If a/b=c/d, then it is written a:b=c:dor a:b::c:d. Also if a/b=c/d=lamdaimpliesa=blamdaand c=dlamdaimpliesa/b=c/d =(a+-c)/(b+-d)=(""^(n)sqrt((a)^(n)+-(c)^(n)))/(""^(n)sqrt((b)^(n)+-(d)^(n)))=lamda(lamdagt0) important property of proportion : 1. If a:b=c:d,then (a+b)/(b)=(c+d)/(d)("Componendo")i.e.(a)/(b)=(c)/(d)implies(a)/(b)+1=(c)/(d)+1 2. If a:b=c"d, then (a-b)/(b)=(c-d)/(d)("Dividenod")i.e.(a)/(b)=(c)/(d)implies(a)/(b)-1=(c)/(d)-1 3. If a:b:=c:d, then (a+b)/(a-b)=(c+d)/(c-d)("Componendo and dividendo") If (x^(3)+x^(2)+x+1)/(x^(3)-x^(2)-x-1)=(x^(2)+x1)/(x^(2)-1+1) then the number of real value of x satisfying are

If f(x)=((a+x)/(b+x))^(a+b+2x) then prove that f'(0)=[2log((a)/(b))+(b^(2)-a^(2))/(ab)]((a)/(b))^(a+b)

Find the value of (x + a)/( x - a) + ( x + b)/( x - b) , if x = (2ab)/( a + b)