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# Add or subtract this rational expressions.

Add or subtract this rational expressions.

(1)

10                7
--------------- + ------------
x^2-16x+60       x^2-100

(2)

3                         2
....................  -    ...............
x^2-6x-16x           x^2-2x-48
Add or subtract this rational expressions.

(1)

10                7
--------------- + ------------
x^2-16x+60       x^2-100

(2)

3                   2
.................... -  ...............
x^2-6x-16x        x^2-2x-48

I seem to recall having done these a few days ago.

### 1 Answer by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
0
1.

10                    7
--------------- + ------------ =
x^2-16x+60         x^2-100

[10/(x2 -16x + 60)] + [7/(x2 - 100)]

Multiply both fractions by (x2 - 16x + 60)*(x2 - 100) to create a common denominator:

[10* (x2 - 100) + 7*(x2 - 16x +60)]/[(x2 - 100)*(x2 - 16x + 60)]

Factor

[10*(x + 10)*(x - 10) + 7*(x - 10)*(x - 6)]/[(x - 10)2*(x + 10)*(x - 6)] =

[10*(x + 10) + 7*(x - 6)]/[(x - 10)(x + 10)*(x - 6)] =

(10*x + 100 + 7x - 42)/[(x - 10)(x + 10)*(x - 6)] =

(17x +58)/[(x - 10)(x + 10)*(x - 6)]

No. 2 can be solved by the same method.

3                    2
.................... - ...............
x^2-6x-16x      x^2-2x-48

I am assuming you meant to type x^2 - 6x - 16 instead of x^2-6x-16x

3*(x2 - 2x - 48)*(x2 - 6x - 16) - 2*(x2 - 2x - 48)*(x2 - 6x - 16)
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(x2 - 2x - 48)*(x2 - 6x - 16)

Factor

3*[(x - 8)*(x + 6)*(x - 8)*(x + 2)] + 2*[(x - 8)*(x + 6)*(x - 8)*(x + 2)]
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[(x - 8)*(x + 6)*(x - 8)*(x + 2)]

(x + 14)/[(x - 8)*(x + 2)*(x + 6)