1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arturiano [62]
2 years ago
12

If a = 1/x+1/y , what is the value of 1/a

Mathematics
2 answers:
kykrilka [37]2 years ago
8 0

We are given that <em>a =(1/x) + (1/y)</em> , and need to find the value of (1/a) , as <em>a</em> is the sum of <em>two fractions</em> so we can't reciprocal both sides <em>directly</em> without <em>finding their sum</em> and converting them into a <em>single fraction</em> . So , let's start by simplifying <em>a</em> first

{:\implies \quad \sf a=\dfrac{1}{x}+\dfrac{1}{y}}

{:\implies \quad \sf a=\dfrac{x+y}{xy}}

Now , we knows an indentity ;

  • {\boxed{\bf{{\left(\dfrac{a}{b}\right)}^{-1}=\dfrac{b}{a}}}}

Now , raising to the <em>power -1</em> on both sides :

{:\implies \quad \sf {\left(\dfrac{a}{1}\right)}^{-1}={\left(\dfrac{x+y}{xy}\right)}^{-1}}

{:\implies \quad \bf \therefore \quad \underline{\underline{\dfrac{1}{a}=\dfrac{xy}{x+y}}}}

lana66690 [7]2 years ago
3 0
<h3>Solution</h3>

a=\frac{1}{x}+\frac{1}{y}

so the value of 1/a is…

\begin{aligned}\frac{1}{a}&=\frac{1}{\frac{1}{x}+\frac{1}{y}}\\&\Rightarrow\frac{1}{\frac{y+x}{xy}}\\&\Rightarrow1\times\frac{xy}{y+x}\\&\Rightarrow\frac{xy}{x+y}\end{aligned}

You might be interested in
Is (1,1) a solution of the system?
xxTIMURxx [149]
Yes it is the solution to the system
3 0
3 years ago
Read 2 more answers
Working a second job _____.
hram777 [196]
I believe it would be all of the above let me know if it is right
7 0
3 years ago
YOU HAVE BEN CHANGING DIESEL DISPENSERS FOR 35 MINS. YOU HAVE 5 SHOWERS THAT NEED TO BE CLEANED. HOW MANY MINUTES SHOULD IT TAKE
ExtremeBDS [4]
Each would take 7 minutes
5 0
3 years ago
Read 2 more answers
Six more than 1/5 a number is 12. What is the number
suter [353]

Answer:

Step-by-step explanation:

let x be the number

6+1/5x=12

1/5x=12-6

1/5x=6

x=5*6

x=30

check: 6+(1/5*30)=6+6=12

8 0
2 years ago
Rewrite the function f(x)=2(x-2)^2-5 and in the form ax^2+bx+c
Ira Lisetskai [31]

Answer:

Step-by-step explanation:

f(x)=2(x-2)²-5

f(x)=2(x²-4x+4)-5

f(x)=2x²-8x+3

7 0
3 years ago
Other questions:
  • PLEASE HELP! Given: AG and BH , transversal CF ∠ADE and _______ are corresponding
    8·2 answers
  • The photography club has 28 members. There are 12 boys in the club. What is the ratio of boys to girls in simplest form?
    14·2 answers
  • I need help with this
    12·1 answer
  • Find the 11th term of the geometric sequence 10, 20, 40, ...10,20,40,
    15·1 answer
  • Help me with this one !!!!!
    14·1 answer
  • a teacher buys a 128-ounce bottle of juice and serves it in 5-ounce cups. What are the possible numbers of cups she can fill?
    6·2 answers
  • (-8)-6+(-5) help ima stuck
    15·2 answers
  • -4(-3x-2)=32 please hurry
    14·1 answer
  • Graph the equations x = 3 and y=5.
    12·1 answer
  • Hello can someone plz help me? Plz show your work
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!