x ² + 9x = x (x + 9), so the partial fraction decomposition would be
(7x + 18) / (x ² + 9x) = a/x + b/(x + 9)
where a, b are some constants. To find them, multiply both sides by x ² + 9x :
7x + 18 = a (x + 9) + bx
Solve for a and b :
7x + 18 = (a + b) x + 9a
[ a + b = 7
[ 9a = 18
→ a = 2, b = 5
So
(7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)
The correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x is 2/x + 5/(x + 9).
Fractions represent equal parts of a whole or a collection. Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
Here,
x ² + 9x = x (x + 9), so the partial fraction decomposition would be
(7x + 18) / (x ² + 9x) = a/x + b/(x + 9)
where a, b are some constants. To find them, multiply both sides by x ² + 9x :
7x + 18 = a (x + 9) + bx
Solve for a and b :
7x + 18 = (a + b) x + 9a
[ a + b = 7
[ 9a = 18
→ a = 2, b = 5
So
(7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)
Learn more about Fractions:
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