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erma4kov [3.2K]
2 years ago
14

Simplify, state all restrictions.

Mathematics
1 answer:
Kipish [7]2 years ago
7 0

The simplified expression is \frac{1 - x - y}{x + y}and the restriction is y \ne -x

<h3>How to simplify the expression?</h3>

The expression is given as:

\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1

Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions

\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1

Rewrite the expression as products

\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1

Cancel out the common factors

\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1

Express 4x^2 - y^2 as (2x - y)(2x + y)

\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1

Cancel out the common factors

\frac{1}{x + y} -1

Take the LCM

\frac{1 - x - y}{x + y}

Hence, the simplified expression is \frac{1 - x - y}{x + y}and the restriction is y \ne -x

Read more about expressions at:

brainly.com/question/723406

#SPJ1

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Norma and Albert both clean pools. Each charges a flat fee to clean a pool. Norma cleans 12 pools in 8 hours and earns $270. Alb
Novosadov [1.4K]

Answer:

1.5 per hour : 1.2 per hour

Step-by-step explanation:

The computation of the ratio is shown below:

For norma, the one pool would be

= 12  pools ÷ 8 hours

= 1.5 per hour

And for albert, the one pool would be

= 9 pools ÷ 7.5 hours

= 1.2 per hour

So the ratio between them is

1.5 per hour : 1.2 per hour

4 0
2 years ago
Jason buys three shirts with a listed price of $20 each. Jason uses a coupon that provides "Buy Two, Get One Free". What is the
Temka [501]

Given:

Jason buys three shirts with a listed price of $20 each.

He uses a coupon that provides "Buy Two, Get One Free".

To find:

The total final price Jason pays.

Solution:

Total number of shirts he buys = 3

Since he uses a coupon that provides "Buy Two, Get One Free", therefore he need to pay for 2 shirts and 1 he will get free.

Cost of 1 shirt = $20

Cost of 2 shirts = 2 × $20

                        = $40

Therefore, total final price Jason pays is $40.

3 0
3 years ago
Exercise 30 please , show work
ArbitrLikvidat [17]
-8(2a-3b)-5(6b-4a)=\\=-8 \times 2a -8 \times (-3b)-5 \times 6b-5 \times (-4a)= \\&#10;=-16a+24b-30b+20a= \\&#10;=20a-16a+24b-30b= \\&#10;=(20-16)a+(24-30)b= \\&#10;=4a-6b
3 0
3 years ago
Read 2 more answers
Please Help! 39 and 40 please!!! :D
Pavel [41]

Answer:

Look below.

Step-by-step explanation:

39.

10+ = 149 times x

3 - 9  = 143 times x

40.

2(w times 1.5 + w)

6 0
3 years ago
Find cottheta If cactus theta = -square root 37/6
OLga [1]
The question is not clear but I will solve it for all the possible conditions.

If cosФ = - √37 ÷ 6

Which means,
Adjacent = - √37
Hypotenuse = 6

This is not possible because hypotenuse cannot be smaller.


If cosecФ = - √37 ÷ 6

Which means,
Opposite = 6 
Hypotenuse = - √37

Using Pythagoras theorem,

Adjacent = (Hypotenuse)² - (Opposite)²

Adjacent = √{(- √37)² - (6)²}

Adjacent = √{(37 - 36}

Adjacent = √{(1}

Adjacent = 1

Now we have all the three sides of a right triangle, therefore, we can find out the value for cotФ.
That is;

cotФ = adjacent ÷ opposite

cotФ = \frac{1}{6}
7 0
3 years ago
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