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lozanna [386]
3 years ago
13

6-5 solving rational equations 8/x+3=1/x+1

Mathematics
1 answer:
AfilCa [17]3 years ago
7 0

Answer:

x = -5/7

Step-by-step explanation:

8/(x+3)=1/(x+1)

Using cross products

8*(x+1) = 1*(x+3)

Distribute

8x+8 = x+3

Subtract x from each side

8x-x +8 = x+3-x

7x +8 =3

Subtract 8 from each side

7x+8-8 = 3-8

7x = -5

Divide by 7

7x/7 = -5/7

x = -5/7

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How do I factor (x^2 + 1)^1/2 +2(x^2 + 1)^1/2
professor190 [17]
(x^{2} + 1)^{ \frac{1}{2}} + 2((x^{2} + 1)^{ -\frac{1}{2}}) \\\\ Take \ out \ (x^{2} + 1)^{ \frac{1}{2}} \ like \ so: \\\\ (x^{2} + 1)^{ \frac{1}{2}}(1 + 2(x^{2} + 1)^{ -1}) \\\\ = (x^{2} + 1)^{ \frac{1}{2}}(1 + \frac{2}{(x^{2} \ + \ 1)}) \\\\ = (x^{2} + 1)^{ \frac{1}{2}}(\frac{2 \ + \ (x^{2} \ + \ 1)}{(x^{2} \ + \ 1)}) \\\\ = (x^{2} + 1)^{ \frac{1}{2}}(\frac{(x^{2} \ + \ 3)}{(x^{2} \ + \ 1)}) \\\\ = \frac{(x^{2} \ + \ 1)^{ \frac{1}{2}}(x^{2} \ + \ 3)}{(x^{2} \ + \ 1)} \\\\
This is what I would think to do with such an expression;
It should be alright to leave it as it is on the last line as this should be its simplest form;
But, you could write it out as:
\frac{(x^{2} \ + \ 3)}{(x^{2} \ + \ 1)^{ \frac{1}{2}}} \\\\
= \frac{(x^{2} \ + \ 3)}{ \sqrt{(x^{2} \ + \ 1)}}
5 0
3 years ago
Which of the following statements about AB and AC is true?
Mumz [18]

Answer: C

Step-by-step explanation:

Ap3x

7 0
3 years ago
A ticket to the fair initially costs $10. The price is increased by 15%. Then, the price is decreased by 25% (from the already i
Fantom [35]
Increased price = $10 + $10×15% = $11.50

decreased price = $11.50 - $11.5×25% = 8.625
7 0
4 years ago
E is the midpoint of DF⎯⎯⎯⎯⎯, DE=6x+1 and EF=7x−4. Find DE, EF, and DF
grandymaker [24]

DE is 31 units, EF is 31 units and DF is 62 units

Step-by-step explanation:

A mid-point of a line segment

  • Divides it into two congruent parts
  • The length of each part is half the length of the line segment

∵ E is the mid-point of segment DF

- That means E divides DF into two parts DE and EF and the

   lengths of them are equal

∴ DE ≅ EF

∵ DE = 6x + 1

∵ EF = 7x - 4

- Equate them

∴ 6x + 1 = 7x - 4

- Add 4 to both sides

∴ 6x + 5 = 7x

- Subtract 6x from both sides

∴ 5 = x

Substitute the value of x in DE and EF to find their length

∵ DE = 6(5) + 1

∵ DE = 30 + 1

∴ DE = 31 units

∵ EF = 7(5) - 4

∴ EF = 35 - 4

∴ EF = 31 units

∵ DF = DE + EF

∴ DF = 31 + 31

∴ DF = 62 units

DE is 31 units, EF is 31 units and DF is 62 units

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

8 0
3 years ago
Help on questions 37 and 38 please!
jeka94

Answer:

Step-by-step explanation:

38.

M=\frac{1}{2} (x_{1}+x_{2})\\2M=x_{1}+x_{2}\\x_{1}=2M-x_{2}

37.

S=\frac{ab^2}{3} \\3S=ab^2\\b^2=\frac{3S}{a} \\b=\pm\sqrt{\frac{3S}{a} }

6 0
3 years ago
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