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
Luba_88 [7]
3 years ago
15

Simplify (x + 2/ x^2 + 2x -3) / (x + 2/x^2 - x)

Mathematics
2 answers:
rjkz [21]3 years ago
5 0

Answer:

The simplest form is x/(x + 3)

Step-by-step explanation:

* To simplify the rational Expression lets revise the factorization

  of the quadratic expression

*  To factor a quadratic in the form x² ± bx ± c:

- First look at the c term  

# If the c term is a positive number, and its factors are r and s they

  will have the same sign and their sum is b.

#  If the c term is a negative number, then either r or s will be negative

   but not both and their difference is b.

- Second look at the b term.  

# If the c term is positive and the b term is positive, then both r and

  s are positive.  

Ex: x² + 5x + 6 = (x + 3)(x + 2)  

# If the c term is positive and the b term is negative, then both r and s

  are negative.  

Ex:  x² - 5x + 6 = (x -3)(x - 2)

# If the c term is negative and the b term is positive, then the factor

  that is positive will have the greater absolute value. That is, if

  |r| > |s|, then r is positive and s is negative.  

Ex: x² + 5x - 6 = (x + 6)(x - 1)

# If the c term is negative and the b term is negative, then the factor

  that is negative will have the greater absolute value. That is, if

  |r| > |s|, then r is negative and s is positive.

Ex: x² - 5x - 6 = (x - 6)(x + 1)

* Now lets solve the problem

- We have two fractions over each other

- Lets simplify the numerator

∵ The numerator is \frac{x+2}{x^{2}+2x-3}

- Factorize its denominator

∵  The denominator = x² + 2x - 3

- The last term is negative then the two brackets have different signs

∵ 3 = 3 × 1

∵ 3 - 1 = 2

∵ The middle term is +ve

∴ -3 = 3 × -1 ⇒ the greatest is +ve

∴ x² + 2x - 3 = (x + 3)(x - 1)

∴ The numerator = \frac{(x+2)}{(x+3)(x-2)}

- Lets simplify the denominator

∵ The denominator is \frac{x+2}{x^{2}-x}

- Factorize its denominator

∵  The denominator = x² - 2x

- Take x as a common factor and divide each term by x

∵ x² ÷ x = x

∵ -x ÷ x = -1

∴ x² - 2x = x(x - 1)

∴ The denominator = \frac{(x+2)}{x(x-1)}

* Now lets write the fraction as a division

∴ The fraction = \frac{x+2}{(x+3)(x-1)} ÷ \frac{x+2}{x(x-1)}

- Change the sign of division and reverse the fraction after it

∴ The fraction = \frac{(x+2)}{(x+3)(x-1)}*\frac{x(x-1)}{(x+2)}

* Now we can cancel the bracket (x + 2) up with same bracket down

 and cancel bracket (x - 1) up with same bracket down

∴ The simplest form = \frac{x}{x+3}

Amanda [17]3 years ago
5 0

ANSWER

\frac{x}{x + 3}

EXPLANATION

We want to simplify:

\frac{x +2 }{ {x}^{2}  + 2x - 3}  \div  \frac{x + 2}{ {x}^{2}- x}

Multiply by the reciprocal of the second fraction:

\frac{x +2 }{ {x}^{2}  + 2x - 3}   \times   \frac{{x}^{2}- x}{ x + 2}

Factor;

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

We cancel out the common factors to get:

\frac{x}{x + 3}

You might be interested in
Which of the following mixed numbers is equivalent to 12.1 6 ?
Sliva [168]
Well, you don't have any options.
But a mixed number for 12.16 would be 12 4/25. Hope it helps! :)
7 0
3 years ago
Read 2 more answers
PLS HELP MEEE !!!!!
kotykmax [81]

Answer:

5 terms

Step-by-step explanation:

x is one term

-3 is one term

2y is one term

-16 is one term

4x is one term

5 terms in total

7 0
3 years ago
Read 2 more answers
PLEASE HELP ME ASAP I REALLY NEED HELP!!!
padilas [110]

1) \overline{UP}

2) \overline{UP} \cong \overline{UP}

3) \overline{UR}

4) \overline{PR}

5) \triangle OUP \cong \triangle RUP by SSS

6) CPCTC

7 0
2 years ago
What fraction of an hour is 10 minutes?<br><br> Give your answer in its simplest form.
Naddika [18.5K]

Answer:

1/6

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The ropes on either side of a swing are 1.9 m long. If a child swings through a arc length of 0.9 Determine the angle (in radian
Yuliya22 [10]

Answer:

theta = 9/19 radians or  approximately .4737 radians

Step-by-step explanation:

The formula for arc length is

S = r theta  

where theta is in radians.  Lets put in what we know.  The radius would be 1.9 since the ropes would be the radius.

.9 = 1.9 theta

Divide by 1.9 on each side.

.9/1.9 = theta

theta = 9/19 radians

or in decimal form it is approximately  .4737 radians



7 0
3 years ago
Other questions:
  • Marcus can walk 1 mile to the library in about the same time he can bicycle 2.5 miles to the sporting good store. His speed on t
    12·1 answer
  • Reduce −2 + b2 by 7 + b2.
    6·2 answers
  • Si n es un número impar, ¿cuál de las siguientes opciones representa un número par? a) 2n +1 b) n (n + 2) c) n + (n-1) e) 2 (n +
    12·1 answer
  • Maya has 8 and 1/10 of cake. She gives 2 and 9/10 of the cake to her friend Alyssa. How much cake does Maya have left.
    12·1 answer
  • What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12?
    7·2 answers
  • 4. 12% of 72 is what number?
    14·2 answers
  • 10) the LAST ONE Use Distributive Property and Combine Like Terms to simplify the expression below HELP PLZ PLZ PLZ
    13·2 answers
  • GIVING BRAINIEST THIS IS 6TH GRADE LEVEL MATH!
    5·1 answer
  • What is cos 0 when sin 0
    12·1 answer
  • Which statement is true about the function f(x) = -√-x?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!