Rational Expressings.. Math help please??

Question

Could someone please help me with these math rational expressings please?? thanks


1) x^2 / x - 1 - 1 / x - 1

2) 4x + y / 2x + 3y - 1 / x - 1

3) x^2 + 3x + 2 / x^2 - 16 + 3x + 6 / n^2 - 16

4) 7 / x - 5 - 2 + x / x - 5

Answer 1

x² / x - 1 - 1 / x - 1 =

x² - 1 / x - 1

(x - 1)(x + 1) / x - 1

x - 1 cancell

x + 1

- - - - - - -s-

Answer 2

1) x^2 / x - 1 - 1 / x - 1=
(x^2-1)/(x-1)=
[(x-1)(x+1)]/(x-1)=
x+1

Answer 3

1) x^2/(x - 1) - 1/(x - 1)

Merge them, since they have a common denominator.

(x^2 - 1)/(x - 1)

Factor the numerator.

[(x - 1)(x + 1)] / (x - 1)

Cancel the common factor of (x - 1).

x + 1

3) (x^2 + 3x + 2) / (x^2 - 16) + (3x + 6)/(x^2 - 16)

Merge into one fraction.

[x^2 + 3x + 2 + 3x + 6] / [x^2 - 16]

Group like terms.

[x^2 + 6x + 8] / [x^2 - 16]

Factor top and bottom.

[(x + 4)(x + 2)] / [(x - 4)(x + 4)]

Cancel the common factor.

(x + 2) / (x - 4)

Answer 4

Hi,

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