Question

factorize x/x-1 + x-1/x = 5/2​

Answer 1

Answer:

STEP

1

:

5

Simplify —

2

Equation at the end of step

1

:

x 1 5

(((—-1)+x)-—)-— = 0

x x 2

STEP

2

:

1

Simplify —

x

Equation at the end of step

2

:

x 1 5

(((— - 1) + x) - —) - — = 0

x x 2

STEP

3

:

x

Simplify —

x

Equation at the end of step

3

:

1 5

(((1 - 1) + x) - —) - — = 0

x 2

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x as the denominator :

x x • x

x = — = —————

1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • x - (1) x2 - 1

——————————— = ——————

x x

Equation at the end of step

4

:

(x2 - 1) 5

———————— - — = 0

x 2

STEP

5

:

Trying to factor as a Difference of Squares

5.1 Factoring: x2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : x2 is the square of x1

Factorization is : (x + 1) • (x - 1)

Answer 2

Step-by-step explanation:

I hope it is helpful to you