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domain of cos(2x+5)

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partial fractions 1(x+5)(x+4)

Solution

−1x+5 +1x+4

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Solution steps

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1(x+5)(x+4)

Create the partial fraction template using the denominator (x+5)(x+4)

1(x+5)(x+4) =a₀x+5 +a₁x+4

Multiply equation by the denominator

1· (x+5)(x+4)(x+5)(x+4) =a₀(x+5)(x+4)x+5 +a₁(x+5)(x+4)x+4

Simplify

1=a₀(x+4)+a₁(x+5)

Solve the unknown parameters by plugging the real roots of the denominator: −5, −4

For the denominator root −5: a₀=−1

For the denominator root −4: a₁=1

a₀=−1, a₁=1

Plug the solutions to the partial fraction parameters to obtain the final result

(−1)x+5 +1x+4

Simplify

−1x+5 +1x+4

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

domain of cos(2x+5)

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