1.

10 7

--------------- + ------------ =

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

[10/(x^{2} -16x + 60)] + [7/(x^{2} - 100)]

Multiply both fractions by (x^{2} - 16x + 60)*(x^{2} - 100) to create a common denominator:

[10* (x^{2} - 100) + 7*(x^{2} - 16x +60)]/[(x^{2} - 100)*(x^{2} - 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*(x^{2} - 2x - 48)*(x^{2} - 6x - 16) - 2*(x^{2} - 2x - 48)*(x^{2} - 6x - 16)

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(x^{2} - 2x - 48)*(x^{2} - 6x - 16)

Factor

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

__________________________________________________________ =

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

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

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