Prove that -a-1-a-1 - b-1 - a-1-a-1 - b-1 - 2b2-b2 - a2

A^ 1/(a)^ 1 + (b)^ 1 + a^ 1/(a)^ 1 (b)^ 1 = 1/a/1/a + 1/b + 1/a/1/a 1/b [a^ m = (1/a)^m] = 1/a/b+a/ab + 1/a/b a/ab = 1/a.ab/b+a + 1/a. ab/b a = ...

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Addition and Subtraction of Algebraic Expressions

Prove that :a...

Question

Prove that :

$\frac{a^{- 1}}{(a)^{- 1} + (b)^{- 1}} + \frac{a^{- 1}}{(a)^{- 1} - (b)^{- 1}} = \frac{2 b^{2}}{b^{2} - a^{2}}$

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\frac{a^{- 1}}{a^{- 1} + b^{- 1}} + \frac{a^{- 1}}{a^{- 1} - b^{- 1}} = \frac{2 b^{2}}{b^{2} - a^{2}}

x = 1 + a + a^{2} + . . . . .

y = 1 + b + b^{2} . . . .

| a | < 1

| b | < 1

1 + a b + a^{2} b^{2} + . . . . = \frac{x y}{x + y - 1}

a \int a f (x) d x = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 2 a \int 0 f (x) d x & if f (x) is an even function 0 & if f (x) is an odd function \end{matrix}

1 \int - 1 {sin}^{5} x {cos}^{4} x d x

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 1 & a b & a c a b & b^{2} + 1 & b c c a & c b & c^{2} + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 1 + a^{2} + b^{2} + c^{2}

a, b, c

a^{2} = b^{2} + c^{2} - 2 b c \sqrt{1 - a^{2}}, b^{2} = c^{2} + a^{2} - 2 c a \sqrt{1 - b^{2}}, c^{2} = a^{2} + b^{2} - 2 a b \sqrt{1 - c^{2}}

a = c \sqrt{1 - b^{2}} + b \sqrt{1 - c^{2}}

If $X = 1 + a + a^{2} + . . . . \infty$ , where |a| < 1 and $y = 1 + b + b^{2} + . . . . . \infty$ where |b| <1,

prove that $1 + a b + a^{2} b^{2} + . . . . . \infty \frac{x y}{x + y - 1}$

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