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Perform the indicated operations and simplify the result. Leave your answer in factored form.

1) x/16 - 1/x all over 1 + 4/x

A) x+4/16
B) x-4/16
C) 16/x+4
D) 16/x-4
E) -16/x+4

I chose answer C. I saw this as x^2-16/ x+4.

Multiply the following using the FOIL method. Express your answer as a single polynomial in standard form.

2) (sqrt a + a)(sqrt a - a)

A) a - a^2
B) a + a^2
C) sqrt a - a^2
D) 2 sqrt a
E) a

Simplify the expression. Express answers so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0.

( 8 x^-1 / 3 y^-1)^-2

A) 9 y^2 / 64 x^2
B) 64 x^2 / 9 y^2
C) 64 y^2 / 9 x^2
D) 9 x^2 / 64 y^2
E) -9 x^2 /64 y^2

I chose answer A) 9 y^2 / 64 x^2

1. first multiply both top and bottom of your fraction by 16x/(16x) to get
(x^2 - 16)/(16x-64)

= (x+4)(x-4)/(16(x-4))
= (x+4)/16 which is probably what you meant when you typed a)

2. (√a + a)(√a - a) = a - a^2 , which is b)

3. ( 8 x^-1 / 3 y^-1)^-2
= [(8/x) / (3/y)]^-2
= [(8/x)(y/3)]^-2
= [(8y)/(3x)]^-2
= [(3x)/(8y)]^2
= 9x^2/(64y^2) or D)

SO for #2 the answer is a-a^2 or +a^2?

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