Question

solution of x+ 1 = 18 and × /2 + 1 = 9 is same​

Answer 1

Step-by-step explanation:

18

Simplify ——

x2

Equation at the end of step

1

:

9 18

((— - 1) + 1) - (—— - 1) = 0

x x2

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x2 as the denominator :

1 1 • x2

1 = — = ——————

1 x2

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 :

2.2 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:

18 - (x2) 18 - x2

————————— = ———————

x2 x2

Equation at the end of step

2

:

9 (18 - x2)

((— - 1) + 1) - ————————— = 0

x x2

STEP

3

:

9

Simplify —

x

Equation at the end of step

3

:

9 (18 - x2)

((— - 1) + 1) - ————————— = 0

x x2

STEP

4

:

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a whole from a fraction

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

1 1 • x

1 = — = —————

1 x

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

9 - (x) 9 - x

——————— = —————

x x

Equation at the end of step

4

:

(9 - x) (18 - x2)

(——————— + 1) - ————————— = 0

x x2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a whole to a fraction

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

1 1 • x

1 = — = —————

1 x

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

(9-x) + x 9

————————— = —

x x

Equation at the end of step

5

:

9 (18 - x2)

— - ————————— = 0

x x2

STEP

6

:

Trying to factor as a Difference of Squares:

6.1 Factoring: 18-x2

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 : 18 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Calculating the Least Common Multiple :

6.2 Find the Least Common Multiple

The left denominator is : x

The right denominator is : x2

Answer 2

Answer:

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