All categories

2 years ago

What is the sum of the rational expressions below? 3x-1/2x + 3x/x-1

Mathematics

2 answers:

Evgen [1.6K]2 years ago

7 0

Answer:

$\frac{9x^2-4x+1}{2x(x-1)}$

Step-by-step explanation:

The given expression is:

$\frac{3x-1}{2x}+\frac{3x}{x-1}$

Simplifying the above expression, we get

$\frac{(3x-1)(x-1)+3x(2x)}{2x(x-1)}$

$\frac{3x^2-x-3x+1+6x^2}{2x(x-1)}$

$\frac{9x^2-4x+1}{2x(x-1)}$

which is the required sum of the given rational expression.

Elden [556K]2 years ago

6 0

In order to find the sum of the given rational expressions above, here are the steps.
Firstly, you need to find the LCM of the least common denominator.
So it would look like this:
3x-1 + 3x (3x-1)(x-1) + (2x)(3x)
------ ------- = ---------------------------
2x x-1 2x(x-1)

3x^2-4x+1+6x^2
----------------------
2x(x-1)
And the final result would be this:
9x^2-4x+1
--------------
2x(x-1)

9x^2-4x+1
--------------
2x^2-2x

Hope that this is the answer that you are looking for.

You might be interested in

Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy. Which of the following is a justification for Step 3 of her

vodka [1.7K]

Solution:

we are given that

Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy.

we have been asked to find

Which of the following is a justification for Step 3 of her proof?

Step 3 of her proof is

$Step 3: (x^2 + xy + xy + y^2) - (x^2 - xy - xy + y^2) = (x^2 + 2xy + y2) - (x^2 - 2xy + y^2)$

As we can observe inside each of the paranthesis only like terms have been added. It mean the required justification is

C. Combining like terms

7 0

2 years ago

The label on the car's antifreeze container claims to protect the car between −40°C and 140°C. To covert Celsius temperature to

sergejj [24]

Answer:

-40 < t < 284

Step-by-step explanation:

The antifreeze protects the car between −40°C and 140°C.

Using t for temperature, the compound inequality of the Celsius temperature range is:

-40 < t < 140

The conversion formula is given to find degrees C in given degrees F. We can solve the formula for F, so we get degrees F in terms of degrees C.

C = (5/9)(F - 32) <------ conversion formula from deg F to deg C

Solve for F:

(9/5)C = F - 32

(9/5)C + 32 = F

F = (9/5)C + 32 <------ conversion formula from deg C to deg F

Now we convert -40 deg C to deg F using the formula we just derived.

F = (9/5)C + 32

F = (9/5)(-40) + 32

F = -72 + 32

F = -40

-40 deg C = -40 deg F

(This is not a mistake or a typo. -40 deg C really is the same as -40 deg F.)

Now we convert 140 deg C to deg F using the formula we just derived.

F = (9/5)C + 32

F = (9/5)(140) + 32

F = 252 + 32

F = 284

140 deg C = 284 deg F

Now we rewrite the compound inequality with Fahrenheit temperatures.

-40 < t < 284

4 0

2 years ago

At her job, Jessie earns $9.50 per hour.

Stolb23 [73]

Answer:

9.50h ≤ 460

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A- 5.57 B- 41 C-12 D-21.71

Kryger [21]

Answer:

Step-by-step explanation:

If KM bisects angle NKL, the angle 3 is congruent to angle 4.

We are given that angle 1 is congruent to angle 2, so that means that angle JKP is congruent to angle PKN. By the definition of an angle bisector, we know then that angle NKM is congruent to angle MKL. By the definition of a straight angle formed by opposite rays, all those angles named above add up to equal 180 degrees. So if angle JKN = 8x + 2 and angle MKL = 3x + 5 and angles NKM and MKL are congruent, then angle NKL = 2(3x + 5) which is 6x + 10. Again, if all those angles above add up to equal 180, then

8x + 2 + 6x + 10 = 180 and

14x + 12 = 180 and

14x = 168 so

x = 12.

Angle MKN = 3x + 5 so if x = 12, then

Angle MKN = 3(12) + 5 and

Angle MKN = 41 degrees

4 0

2 years ago

at what x coordinate would a line whose equation is y=2x-3 intersect a perpendicular line whose y intercept is 17

Jlenok [28]

Answer:

Step-by-step explanation:hj

4 0

1 year ago