a^-1/a^-1+b^-1 is equal to : 1. b/a+b 2. a+b/a 3. a/a+b 4. a(a + b)

Simplifying the expression : Hence, Option 1 is the correct option.

Mathematics

$\dfrac{a^{-1}}{a^{-1} + b^{-1}}$ is equal to :
$\dfrac{b}{a + b}$
$\dfrac{a + b}{a}$
$\dfrac{a}{a + b}$
a(a + b)

Indices

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Answer

Simplifying the expression :

$\Rightarrow \dfrac{a^{-1}}{a^{-1} + b^{-1}} = \dfrac{\dfrac{1}{a}}{\dfrac{1}{a} + \dfrac{1}{b}} \\[1em] = \dfrac{\dfrac{1}{a}}{\dfrac{b + a}{ab}} \\[1em] = \dfrac{ab}{a(b + a)} \\[1em] = \dfrac{b}{a + b}.$

Hence, Option 1 is the correct option.

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Mathematics

$\dfrac{a^{-1}}{a^{-1} + b^{-1}}$ is equal to :
$\dfrac{b}{a + b}$
$\dfrac{a + b}{a}$
$\dfrac{a}{a + b}$
a(a + b)

Indices

Answer

Related Questions

Simplify :
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Simplify :
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Mathematics

a−1a−1+b−1\dfrac{a^{-1}}{a^{-1} + b^{-1}}a−1+b−1a−1​ is equal to :ba+b\dfrac{b}{a + b}a+bb​a+ba\dfrac{a + b}{a}aa+b​aa+b\dfrac{a}{a + b}a+ba​a(a + b)

Indices

Answer

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Simplify :(xaxb)a2+ab+b2×(xbxc)b2+bc+c2×(xcxa)c2+ca+a2\Big(\dfrac{x^a}{x^b}\Big)^{a^2 + ab + b^2} \times \Big(\dfrac{x^b}{x^c}\Big)^{b^2 + bc + c^2} \times \Big(\dfrac{x^c}{x^a}\Big)^{c^2 + ca + a^2}(xbxa​)a2+ab+b2×(xcxb​)b2+bc+c2×(xaxc​)c2+ca+a2

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3xy−1+2yx−1\dfrac{3x}{y^{-1}} + \dfrac{2y}{x^{-1}}y−13x​+x−12y​ is equal to :6xy3x2 + 2y25xy6xy\dfrac{6}{xy}xy6​

$\dfrac{a^{-1}}{a^{-1} + b^{-1}}$ is equal to :
$\dfrac{b}{a + b}$
$\dfrac{a + b}{a}$
$\dfrac{a}{a + b}$
a(a + b)

Simplify :
$\Big(\dfrac{x^a}{x^b}\Big)^{a^2 + ab + b^2} \times \Big(\dfrac{x^b}{x^c}\Big)^{b^2 + bc + c^2} \times \Big(\dfrac{x^c}{x^a}\Big)^{c^2 + ca + a^2}$

Simplify :
$\Big(\dfrac{x^a}{x^{-b}}\Big)^{a^2 - ab + b^2} \times \Big(\dfrac{x^b}{x^{-c}}\Big)^{b^2 - bc + c^2} \times \Big(\dfrac{x^c}{x^{-a}}\Big)^{c^2 - ca + a^2}$

If $4^{2x} = \dfrac{1}{32}$ , the value of x is :
1.25
-1.25
1
-1

$\dfrac{3x}{y^{-1}} + \dfrac{2y}{x^{-1}}$ is equal to :
6xy
3x² + 2y²
5xy
$\dfrac{6}{xy}$