Steve S. answered • 03/29/14

Tutoring in Precalculus, Trig, and Differential Calculus

= (x-y)^2/((x-y)(x+y)) + (x+y)^2/((x+y)(x-y))

= ((x-y)^2 + (x+y)^2)/((x+y)(x-y))

= (x^2-2xy+y^2 + x^2+2xy+y^2)/(x^2-y^2)

= 2(x^2+y^2)/(x^2-y^2)

NOTICE MINUS SIGN IN DENOMINATOR

2. solve 12x^2 + 7x = 10

12x^2 + 7x – 10 = 0

(ax+b)(cx+d)=(ac)x^2+(ad+bc)x+(bd)

ad and bc are factors of (ac)(bd)

12(-10)=-120

1(-120)

2(-60)

3(-40)

4(-30)

5(-24)

6(-20)

8(-15)

-8(15) <= use these

12x^2 – 8x + 15x – 10 = 0

Factor by Grouping:

(12x^2 – 8x) + (15x – 10) = 0

Take out Greatest Common Factors:

(12x^2 – 8x) + (15x – 10) = 0

4x(3x - 2) + 5(3x - 2) = 0

Both terms have common factor of 3x-2:

(3x - 2)(4x + 5) = 0

Use Zero Product Property:

3x-2 = 0 or 4x+5 = 0

x = 2/3 or x = –5/4

3. Simplify f(x) = (x^2 - 5x + 4)/(x - 1)

Can’t divide by zero, so x ≠ 1.

f(x) = (x - 4) (x - 1) / (x - 1)

Notice that (x-1)/(x-1) = 1 if x ≠ 1,

but (x-1)/(x-1) is UNDEFINED if x = 1.

So the simplified f(x) MUST have the

constraint x ≠ 1 as part of its definition.

f(x) = x - 4, x ≠ 1

4. simplify f(x) = (9x^2 - 3x)/(3x)

Can’t divide by zero, so x ≠ 0.

f(x) = (3x)^2/(3x) - (3x)/(3x), x ≠ 0

Again, x/x = {1 if x ≠ 0, UNDEFINED if x = 0}

f(x) = 3x - 1, x ≠ 0.

Steve S.

03/29/14