Simplification of expression is one type of algebraic expression solver. It is always preferable to keep an algebraic expression as short as possible. In many cases an algebraic expression can be modified to an easier or simpler form so that it is presentable in a better way. There are many processes by which this can be achieved. The general term used to modify an algebraic expression into a simpler form is called as simplify the algebraic expression. Factoring is converting a given expression into a product of two or more
factors. In a rational expression many times you may find common
factors between the numerator and denominator and those factors can be
cancelled. It becomes an additional simplification of the original
expression.

Many algebraic identities help us in factoring and simplifying algebraic expressions directly.

2. x

3. x

4. x

Given $\frac{x^2 + 5x - 36}{x^2 - 2x - 8}$

Step 1:

Factorized the numerator and denominator

x^{2} + 5x - 36 = x^{2} + 9x - 4x - 36

= x(x + 9) - 4(x + 9)

= (x - 4)(x + 9)

=> x^{2} + 5x - 36 = (x - 4)(x + 9)

and x^{2} - 2x - 8 = x^{2} - 4x + 2x - 8

= x(x - 4) + 2(x - 4)

= (x + 2)(x - 4)

=> x^{2} - 2x - 8 = (x + 2)(x - 4)

Step 2:

=> $\frac{x^2 + 5x - 36}{x^2 - 2x - 8}$ = $\frac{ (x - 4)(x + 9)}{ (x + 2)(x - 4)}$

= $\frac{ x + 9}{ x + 2}$

=> $\frac{x^2 + 5x - 36}{x^2 - 2x - 8}$ = $\frac{ x + 9}{ x + 2}$.**answer**

Step 1:

Factorized the numerator and denominator

x

= x(x + 9) - 4(x + 9)

= (x - 4)(x + 9)

=> x

and x

= x(x - 4) + 2(x - 4)

= (x + 2)(x - 4)

=> x

Step 2:

=> $\frac{x^2 + 5x - 36}{x^2 - 2x - 8}$ = $\frac{ (x - 4)(x + 9)}{ (x + 2)(x - 4)}$

= $\frac{ x + 9}{ x + 2}$

=> $\frac{x^2 + 5x - 36}{x^2 - 2x - 8}$ = $\frac{ x + 9}{ x + 2}$.

Given quadratic expression x

There is no any common factor.

Split the middle term – 3x as, – 2x – x. That is,

=> x

Now find ‘x’ is a common factor for the first two terms and -1 as the common factor for the last two terms.

By partial factoring

=> x

Now we see the expression (x – 2) is common factor and using that as a factor,

=> x(x – 2) – 1(x – 2) = (x – 2)(x – 1).

Thus, we ultimately find that x

(x – 2)(x – 1).

=> x

Given

$\frac{x ^2 – 3x + 2}{x^2 – 4}$ is the given rational expression.

Step 1:

Factorized the numerator and denominator

=> x^{2} - 3x + 2 = x^{2} - 2x - x + 2

= x(x - 2) - (x - 2)

= (x - 1)(x - 2)

=> x^{2} - 3x + 2 = (x - 1)(x - 2)

and x^{2} - 4 = x^{2} - 2^{2}

= (x - 2)(x + 2)

[ a^{2} - b^{2} = (a - b)(a + b) ]

=> x^{2} - 4 = (x - 2)(x + 2)

Step 2:

$\frac{x^2 - 3x + 2}{x^2 - 4}$ = $\frac{(x - 1)(x - 2)}{(x - 2)(x + 2)} $

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

With an assumption that x ≠ 2, we can cancel the common term (x – 2).

=> $\frac{ x^2 – 3x + 2}{x^2 – 4}$ = $\frac{ x - 1}{x + 2}$.**answer**

$\frac{x ^2 – 3x + 2}{x^2 – 4}$ is the given rational expression.

Step 1:

Factorized the numerator and denominator

=> x

= x(x - 2) - (x - 2)

= (x - 1)(x - 2)

=> x

and x

= (x - 2)(x + 2)

[ a

=> x

Step 2:

$\frac{x^2 - 3x + 2}{x^2 - 4}$ = $\frac{(x - 1)(x - 2)}{(x - 2)(x + 2)} $

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

With an assumption that x ≠ 2, we can cancel the common term (x – 2).

=> $\frac{ x^2 – 3x + 2}{x^2 – 4}$ = $\frac{ x - 1}{x + 2}$.