Simplify fully
6x2 +x–1 4x2 – 1

3x−1

Step-by-step explanation:

1 Split the second term in 6{x}^{2}+x-16x

2

+x−1 into two terms.

\frac{6{x}^{2}+3x-2x-1}{4{x}^{2}-1}

4x

2

−1

6x

2

+3x−2x−1

2 Factor out common terms in the first two terms, then in the last two terms.

\frac{3x(2x+1)-(2x+1)}{4{x}^{2}-1}

4x

2

−1

3x(2x+1)−(2x+1)

3 Factor out the common term 2x+12x+1.

\frac{(2x+1)(3x-1)}{4{x}^{2}-1}

4x

2

−1

(2x+1)(3x−1)

4 Rewrite 4{x}^{2}-14x

2

−1 in the form {a}^{2}-{b}^{2}a

2

−b

2

, where a=2xa=2x and b=1b=1.

\frac{(2x+1)(3x-1)}{{(2x)}^{2}-{1}^{2}}

(2x)

2

−1

2

(2x+1)(3x−1)

5 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b).

\frac{(2x+1)(3x-1)}{(2x+1)(2x-1)}

(2x+1)(2x−1)

(2x+1)(3x−1)

6 Cancel 2x+12x+1.

\frac{3x-1}{2x-1}

2x−1

3x−1

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36

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