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
MrRa [10]
3 years ago
11

Simplify :Stepwise answer! ​

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
3 0

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{14 {x}^{2}  - 96}{ {x}^{4} - 13 {x}^{2}   + 36}}}}}}

Step-by-step explanation:

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

⇒\sf{ \frac{2(x - 3)(x + 3)(x + 2) + (x - 2)(x + 2)(x  + 3) - 2(x - 2)(x - 3)(x + 3) - (x - 2)(x  +  2)(x - 3)}{(x - 2)(x - 3)(x + 2)(x + 3)}}

Use the formula : a² - b² = ( a + b ) ( a - b )

⇒\sf{ \frac{2( {x}^{2}  - 9)(x + 2) + ( {x}^{2} - 4)(x + 3) - (2x - 4)( {x}^{2} - 9) - ( {x}^{2}   - 4)(x - 3) }{( {x}^{2}  - 4)( {x}^{2}  - 9)}}

Distribute 2 through the parentheses

⇒\sf{ \frac{(2 {x}^{2} - 18)(x + 2) + ( {x}^{2}  - 4)(x + 3) - (2x - 4)( {x}^{2}  - 9) - ( {x}^{2}   - 4)(x - 3)}{( {x}^{2}  - 4)( {x}^{2} - 9) }  }

Multiply the algebraic expressions

⇒\sf{ \frac{2 {x}^{3} + 4 {x}^{2}  - 18x - 36 +  {x}^{3}   + 3 {x}^{2} - 4x - 12 - (2 {x}^{3}  - 18x - 4 {x}^{2}   + 36) - ( {x}^{3} - 3 {x}^{2}  - 4x + 12) } {( {x}^{2}  - 4)( {x}^{2}  - 9)} }

When there is a ( - ) in front of an expression, change the sign of each term in the expression

⇒\sf{ \frac{2 {x}^{3} + 4 {x}^{2} - 18x - 36  +  {x}^{3} + 3 {x}^{2}    - 4x - 12 - 2 {x}^{3}   + 18x + 4 {x}^{2}  - 36 -  {x}^{3}  + 3 {x}^{2}  + 4x - 12}{( {x}^{2} - 4)( {x}^{2}  - 9) } }

Since two opposites add up to zero, it would be better to remove them from the expression

⇒\sf{ \frac{4 {x}^{2}  - 36 + 3 {x}^{2}  - 12 + 4 {x}^{2}  - 36 + 3 {x}^{2}   - 12}{( {x}^{2}  - 4)( {x}^{2}  - 9)} }

collect like terms and simplify

⇒\sf{ \frac{14 {x}^{2}  - 48 - 36 - 12}{( {x}^{2} - 4)( {x}^{2} - 9)  } }

⇒\sf{ \frac{14 {x}^{2}  - 84 - 12}{( {x}^{2}  - 4)( {x}^{2} - 9) } }

⇒\sf{ \frac{14 {x}^{2}  - 96}{ ({x}^{2} - 4)( {x}^{2}  - 9)}  }

Multiply : ( x² - 4 ) and ( x² - 9 )

⇒\sf{ \frac{14 {x}^{2}  - 96}{ {x}^{4}  - 13 {x}^{2}  + 36}}

Hope I helped!

Best regards! :D

You might be interested in
CAN SOMEONE PLEASE HELP ME PLEASE
ioda

Answer:

4, 6/9    sry if wrong

Step-by-step explanation:

6 0
3 years ago
What are some ways you can make a rectangle 10,000 cm squared (I NEED A AWNSER QUICK)​
lidiya [134]

Answer:

2 longer sides would be 4000 each, so that's 8000 total

and the 2 shorter sides could be 1000 each, so that's 2000 total

8000+2000=10,000

Step-by-step explanation:

8 0
3 years ago
2. Simplify:<br> b. 3(2x + 4y)
Nutka1998 [239]

Answer:

(6x+12y)

Step-by-step explanation:

answer is helpful or not

3 0
3 years ago
Read 2 more answers
Find area of the circle
noname [10]
37.68 is the answer

Hope this helped! ^_^
4 0
3 years ago
Read 2 more answers
Hook a brother up please
zzz [600]

Answer: v = 13920 cm cubed

8 0
3 years ago
Other questions:
  • I need help understanding how to do this
    5·1 answer
  • The point P(12.-18) is reflected over the y-axis, what are the coordinates of the
    7·1 answer
  • How many sides does a polygon have with an interior angle of 108?
    5·1 answer
  • What is the value of the expression? 6/10 X 2/8
    7·1 answer
  • ASAP BRAINLIEST What are the main differences between agricultural and hunting/gathering economies?
    11·1 answer
  • Round 2.1132 to the nearest hundredth.<br> Answer:
    5·2 answers
  • The aos of x=2?????????
    9·1 answer
  • -5b = -20 b= need help with homwork
    15·2 answers
  • victor are 60 de lei si merge la florarie pentru a-i cumpara mamei sale un buchet de flori. daca ar cumpara 9 garoafe si 4 trand
    8·1 answer
  • 3(9z+4) &gt; 35z - 4<br> What is z
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!