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Simplify (6x^2-7x-5)/(3-x)

User Yftach
by
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1 Answer

10 votes

Answer:

Simplify —

3

Equation at the end of step

1

:

5

(((6 • (x2)) - 7x) - —) - x

3

STEP

2

:

Equation at the end of step

2

:

5

(((2•3x2) - 7x) - —) - x

3

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 3 as the denominator :

6x2 - 7x (6x2 - 7x) • 3

6x2 - 7x = ———————— = ——————————————

1 3

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

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

6x2 - 7x = x • (6x - 7)

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 • (6x-7) • 3 - (5) 18x2 - 21x - 5

———————————————————— = ——————————————

3 3

Equation at the end of step

4

:

(18x2 - 21x - 5)

———————————————— - x

3

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

x x • 3

x = — = —————

1 3

Trying to factor by splitting the middle term

5.2 Factoring 18x2 - 21x - 5

The first term is, 18x2 its coefficient is 18 .

The middle term is, -21x its coefficient is -21 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 18 • -5 = -90

Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -21 .

-90 + 1 = -89

-45 + 2 = -43

-30 + 3 = -27

-18 + 5 = -13

-15 + 6 = -9

-10 + 9 = -1

-9 + 10 = 1

-6 + 15 = 9

-5 + 18 = 13

-3 + 30 = 27

-2 + 45 = 43

-1 + 90 = 89

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3 Adding up the two equivalent fractions

(18x2-21x-5) - (x • 3) 18x2 - 24x - 5

—————————————————————— = ——————————————

3 3

Trying to factor by splitting the middle term

5.4 Factoring 18x2 - 24x - 5

The first term is, 18x2 its coefficient is 18 .

The middle term is, -24x its coefficient is -24 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 18 • -5 = -90

Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -24 .

-90 + 1 = -89

-45 + 2 = -43

-30 + 3 = -27

-18 + 5 = -13

-15 + 6 = -9

-10 + 9 = -1

-9 + 10 = 1

-6 + 15 = 9

-5 + 18 = 13

-3 + 30 = 27

-2 + 45 = 43

-1 + 90 = 89

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

18x2 - 24x - 5

——————————————

3

Explanation:

User Jay Edwards
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