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### Assignment 10

Solve:

### Solution

Both denominators cannot be equal to for any value of . So, the inequality is valid for all .

We take the right-hand side to the left:

We convert fractions to the same denominator and get:

The factors in the denominator are positive for all (exponential functions) and thus the inequality is valid if the numerator is greater than . Thus:

The numerator in the left-hand side is a quadratic function in and the solutions are (-formula):

The graph of the quadratic function is an 'opens up' parabola and is positive if:

or:

The first inequality is not possible because the right-hand side is negative and the left-hand side is an exponential function which is always positive.

Thus we use the logarithm in the left- and right-hand side and get:

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