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
lana [24]
3 years ago
9

Which expression is equivalent to StartFraction 2 a + 1 Over 10 a minus 5 Endfraction divided by StartFraction 10 a Over 4 a squ

ared minus 1 EndFraction?
Mathematics
1 answer:
const2013 [10]3 years ago
4 0

Answer:

\frac{(2a + 1)^2}{50a}

Step-by-step explanation:

Given

\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1}

Required

Find the equivalent

We start by changing the / to *

\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1}

\frac{2a + 1}{10a - 5} * \frac{4a^2 - 1}{10a}

Factorize 10a - 5

\frac{2a + 1}{5(2a - 1)} * \frac{4a^2 - 1}{10a}

Expand 4a² - 1

\frac{2a + 1}{5(2a - 1)} * \frac{(2a)^2 - 1}{10a}

\frac{2a + 1}{5(2a - 1)} * \frac{(2a)^2 - 1^2}{10a}

Express (2a)² - 1² as a difference of two squares

Difference of two squares is such that: a^2- b^2= (a+b)(a-b)

The expression becomes

\frac{2a + 1}{5(2a - 1)} * \frac{(2a - 1)(2a + 1)}{10a}

Combine both fractions to form a single fraction

\frac{(2a + 1)(2a - 1)(2a + 1)}{5(2a - 1)10a}

Divide the numerator and denominator by 2a - 1

\frac{(2a + 1)((2a + 1)}{5*10a}

Simplify the numerator

\frac{(2a + 1)^2}{5*10a}

\frac{(2a + 1)^2}{50a}

Hence,

\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1} = \frac{(2a + 1)^2}{50a}

You might be interested in
Adding&subtracting equations x-10=12
Colt1911 [192]
Answer:22
x-10=12
x= 10+12
x=22
8 0
2 years ago
Read 2 more answers
Find the range of the data set 145, 612, 120, 349, 515, 212, 590.
storchak [24]

Answer:

The biggest - the smallest

612-120=492

6 0
2 years ago
Read 2 more answers
What is the probability of obtaining 3 heads and 1 tail (order irrelevant) on four flips of a fair coin?
dem82 [27]

1/2 probability of 1 flip

1/2 x 1/2 x 1/2 x 1/2 = 1/16 probability

8 0
3 years ago
PLEASE HELP!
Kay [80]

Answer:

77 inches

Step-by-step explanation:

Given

1 inch = 3 miles in map

We are also given the actual distance between City A and City B = 231 miles.

In order to get the distance in inches = Distance between City A and City B in miles/ 3

We are dividing the distance by 3 to get the distance in inches.

So,

Distance on map = 231/3

= 77 inches

4 0
3 years ago
Read 2 more answers
How do i total this please help<br> 8.3m<br> 5.2m<br> 4.36m<br> 42.1m<br> 86.1m
I am Lyosha [343]
Add them all up so it would equal 146.06
3 0
2 years ago
Other questions:
  • Find the exact values of sin A and cos A. Write fractions in lowest terms. A right triangle ABC is shown. Leg AC has length 21,
    13·2 answers
  • You are going to mix a gallon bucket of window cleaner. The instructions direct you to mix 1 part cleaner to 3 parts water. How
    13·1 answer
  • 25 Points. Please help me out. This is the second to last question I need for the night and then I can go to sleep.
    8·1 answer
  • the lengths of three pieces of wire are in the ratio 10:15:8. if the length of the shortest piece of wire is 2.4 m, find the dif
    6·1 answer
  • In what form is the following linear equation written?
    7·1 answer
  • What is the correct answer for this problem?Explain
    8·2 answers
  • Please help with questions.
    15·1 answer
  • 1. To which set of numbers does the number belong? –55 (1 point) natural numbers / whole numbers/ integers / irrational numbers
    12·2 answers
  • A car travels a distance of 1280 metres at an average speed of 64 kilometres per hour.
    15·1 answer
  • Please solve correctly
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!