Question

Reduce to lowest terms: (Equation In Comments)

Answer 1

\[\frac{ 2^{2}-3x-2 }{ 10+x-3x ^{2} }\]

Answer 2

Thats 2x to the second power above sorry

Answer 3

The numerator 2x^2 -3x -2 can be factored by grouping:

The coefficient of 2 multiplied by -2 = -4. We need 2 numbers so that when multiplied = -4 and the sum = -3. (-3x is the 2nd term in the numerator.)

1(-4) = -4

1-4 =-3

Since -4x + 1x = -3x

This can be re-written as 2x^2 -4x +x -2 when factored by grouping we get

2x(x - 2) +1(x - 2) when factored further we get (2x + 1)(x -2)

Answer 4

The denominator can be re-written as -3x^2 + x + 10

-3(10) = -30

-5(6) = -30

-5 + 6 = 1

Therefore it can be re-written as -3x^2 +6x -5x + 10

When factored it equals -3x(x - 2) -5(x - 2)

When factored further it equals (-3x - 5)(x - 2)

Answer 5

So we get
\[\frac{ (2x + 1)(x - 2) }{ -1(3x + 5)(x -2) }\]

the x - 2 in the numerator and denominator cancel each other out

Answer 6

Thank you very much!