Question

(p+5) -(p-9)+(p-7) reduces to ​

Answer 1

Answer:

Solution

+

7

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Answer 2

Answer:

p=3/2=1.500

Step-by-step explanation:

STEP

1

:

3

Simplify —

p

Equation at the end of step

1

:

3

(6p - —) - 7 = 0

p

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

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

6p 6p • p

6p = —— = ——————

1 p

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:

6p • p - (3) 6p2 - 3

———————————— = ———————

p p

Equation at the end of step

2

:

(6p2 - 3)

————————— - 7 = 0

p

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

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

7 7 • p

7 = — = —————

1 p

STEP

4

:

Pulling out like terms :

4.1 Pull out like factors :

6p2 - 3 = 3 • (2p2 - 1)

Trying to factor as a Difference of Squares:

4.2 Factoring: 2p2 - 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.

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