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
Restaurants often slip takeout menus under Meg's apartment door. So far, Meg has collected 18 menus, including 8 for Chinese foo
Kryger [21]

Answer:

m

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Select the missing numbers. Remember to indicate a negative cash flow with parentheses.
cluponka [151]

To find the cash flow, subtract the Cash Disbursements from the sales receipts for each month.


January: 110 - 135 =  -$25

February: 85 - 110 = -$25

March: 100 - 95 = $5

April: 130 - 95 = $35

May: 145 - 100 = $45

June: 165 - 105 = $60

4 0
3 years ago
Which of the following sets represents a function?
gogolik [260]
It would be D 
Your welcome ;)
5 0
3 years ago
Read 2 more answers
spencer spent 4 hours doing chores over the weekend. If he spent 2/3 for an hour on each chore, how many chores did he do.
Elina [12.6K]
2/3 + 2/3 + 2/3 + 2/3
8/3
2 2/3
4 0
3 years ago
Find the area of a rectangle with the given base and height<br> 5ft,6 in
anygoal [31]

Answer:

360 inch

Step-by-step explanation:

Step 1: Converting

6inch = 6inch

5ft = 60inch

Step 2: Finding the area

Area of a rectangle = L x B

A = 6 x 60

A = 360inch

8 0
3 years ago
Other questions:
  • 2x-4=10 reverse order algebra
    9·1 answer
  • The selling price of a​ refrigerator, is ​$ 468.60. If the markup is 10 % 10% of the​ dealer's cost, what is the​ dealer's cost
    12·1 answer
  • If the mass of your father is 70kg, what is his weight (N)?
    11·1 answer
  • Can 39/121 be simplified and if so what is it??
    9·1 answer
  • There are 575 fireworks to be shot off in a firework display every minute 12 new fireworks are shot off display write a verbal m
    15·1 answer
  • Y+4x=0 how can I solve to know if it's a direct variation?
    5·1 answer
  • Syke Under Shield
    7·1 answer
  • What was the location of the Louisiana Purchase?
    5·2 answers
  • Please answer
    12·1 answer
  • Which ordered pair is shown on the graph?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!