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In this lesson, we will learn how to add and subtract rational expressions, how to identify the domain of the resulting functions, and how to simplify them.

Q1:

Simplify the function π ( π₯ ) = β 8 π₯ β 6 + π₯ β 6 π₯ β 6 π₯ 2 , and determine its domain.

Q2:

Simplify the function π ( π₯ ) = π₯ β 7 π₯ β 3 π₯ β 2 8 β π₯ β 7 7 β π₯ 2 , and determine its domain.

Q3:

Answer the following questions for the rational expressions π₯ + 3 3 and π₯ β 8 2 π₯ .

Find the sum of π₯ + 3 3 and π₯ β 8 2 π₯ .

Is the sum of π₯ + 3 3 and π₯ β 8 2 π₯ a rational expression?

Would this be true for any two rational expressions summed together?

Q4:

Simplify the function π ( π₯ ) = 7 π₯ π₯ β 1 + 3 π₯ 1 β π₯ 2 , and determine its domain.

Q5:

Simplify the function π ( π₯ ) = π₯ + 7 π₯ + 6 + π₯ 3 π₯ , and determine its domain.

Q6:

Simplify the function π ( π₯ ) = 3 π₯ π₯ + 4 β 7 π₯ π₯ β 4 , and determine its domain.

Q7:

Given that the domain of the function π ( π₯ ) = π π₯ + 6 π₯ + π is β β { β 4 , 0 } , and π ( β 1 ) = 2 , find the values of π and π .

Q8:

Simplify the function π ( π₯ ) = 8 π₯ + 7 π₯ β 1 4 π₯ + 4 5 + 3 π₯ β 2 4 π₯ β 1 7 π₯ + 7 2 2 2 , and determine its domain.

Q9:

Simplify the function π ( π₯ ) = π₯ + π₯ + 1 π₯ β 1 β 8 1 β π₯ π₯ β 1 0 π₯ + 9 2 3 2 2 , and determine its domain.

Q10:

Answer the following questions for the rational expressions 5 π₯ β 2 3 π₯ and 3 π₯ β 2 π₯ 2 π₯ + 8 ο¨ .

Subtract 5 π₯ β 2 3 π₯ from 3 π₯ β 2 π₯ 2 π₯ + 8 ο¨ .

Is the difference between 3 π₯ β 2 π₯ 2 π₯ + 8 ο¨ and 5 π₯ β 2 3 π₯ a rational expression?

Is the result of this subtraction a rational expression?

Q11:

Simplify the function π ( π₯ ) = 9 π₯ + 6 + 9 π₯ β 6 , and determine its domain in β .

Q12:

Simplify the function π ( π₯ ) = 5 π₯ π₯ β 4 β π₯ + 4 π₯ β 1 6 2 , and determine its domain.

Q13:

Simplify the function π ( π₯ ) = π₯ + 3 π₯ β 4 9 β 3 π₯ + 2 1 π₯ 3 π₯ β 6 π₯ β 1 0 5 π₯ 2 3 2 4 3 2 , and determine its domain.

Q14:

Simplify the function π ( π₯ ) = π₯ + 1 3 π₯ β π₯ 3 π₯ β 8 , and determine its domain.

Q15:

Simplify the function π ( π₯ ) = ( π₯ β 8 ) β π₯ π₯ + 8 2 , and determine its domain.

Q16:

Simplify the function π ( π₯ ) = 6 4 π₯ β 1 + 9 9 π₯ β 1 8 π₯ 2 2 , and determine its domain.

Q17:

Simplify the function π ( π₯ ) = β 5 π₯ + 8 + 7 π₯ + 4 6 4 β π₯ 2 , and determine its domain.

Q18:

Simplify the function π ( π₯ ) = π₯ β 6 8 π₯ β 5 7 π₯ + 5 4 + π₯ β 5 8 1 π₯ β 8 1 β 8 π₯ 2 2 , and determine its domain.

Q19:

Simplify the function π ( π₯ ) = π₯ β 4 π₯ β 3 2 π₯ β 1 6 π₯ + 6 4 + π₯ β 8 π₯ + 1 2 π₯ β 1 0 π₯ + 1 6 2 2 2 2 , and determine its domain.

Q20:

Simplify the function π ( π₯ ) = π₯ β 7 6 π₯ β 3 5 π₯ β 4 9 + π₯ + 2 1 4 + 1 9 π₯ + 6 π₯ 2 2 , and determine its domain.

Q21:

Given that the domain of the function π ( π₯ ) = 2 π₯ ( π₯ β π ) ( π₯ + 6 ) + 5 π₯ + 5 ( π₯ β π ) ( π₯ + 3 ) is β β { β 6 , β 3 , 2 } , what is the value of π ?

Q22:

Simplify the function π ( π₯ ) = οΌ 4 π₯ β 8 π₯ + 2 π₯ β 8 + 2 π₯ + 4 π₯ + 4 ο Γ π₯ + 2 7 π₯ β 3 π₯ + 9 2 3 2 , and find its domain.

Q23:

Simplify 5 π₯ β 2 3 π₯ β 7 π₯ β 2 9 π₯ 2 4 .

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