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

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

- 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 =

- Lets simplify the denominator

∵ The denominator is

- 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 =

* Now lets write the fraction as a division

∴ The fraction = ÷

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

∴ The fraction =

* 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 =

ANSWER

EXPLANATION

We want to simplify:

Multiply by the reciprocal of the second fraction:

Factor;

We cancel out the common factors to get:

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

step-by-step explanation:

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00