Advertisements
Advertisements
Question
Prove that: `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`
Advertisements
Solution
`a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`
L.H.S. = `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1)`
= `(1/a)/(1/a + 1/b) + (1/a)/(1/a - 1/b)`
= `(1/a)/((b + a)/(ab)) + (1/a)/((b - a)/(ab))`
= `1/a xx (ab)/(b+ a) + 1/a xx (ab)/(b - a)`
= `b/( b + a ) + b/(b - a)`
= `( b^2 - ab + b^2 + ab )/( b^2 - a^2 )`
= `( 2b^2 )/( b^2 - a^2 )`
= R.H.S.
APPEARS IN
RELATED QUESTIONS
If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`
Show that : m - n = 1.
Evaluate :
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`
Simplify : `2{m-3(n+overline(m-2n))}`
Simplify : `"p"^2"x"-2{"px"-3"x"("x"^2-overline(3"a"-"x"^2))}`
Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`
Write each of the following in the simplest form:
(a3)5 x a4
Write each of the following in the simplest form:
a-3 x a2 x a0
Simplify the following and express with positive index:
`[("p"^-3)^(2/3)]^(1/2)`
Simplify the following:
`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`
Simplify the following:
`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`
