Solve for d 16/(d+9)-12/(d^2-81)=10/(d-9)

Math
16d+9-12d2-81=10d-9
Factor each term.
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Rewrite 81 as 92.
16d+9-12d2-92=10d-9
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=d and b=9.
16d+9-12(d+9)(d-9)=10d-9
16d+9-12(d+9)(d-9)=10d-9
Find the LCD of the terms in the equation.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
d+9,(d+9)(d-9),d-9
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 1,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
1
The factor for d+9 is d+9 itself.
(d+9)=d+9
(d+9) occurs 1 time.
The factor for d-9 is d-9 itself.
(d-9)=d-9
(d-9) occurs 1 time.
The LCM of d+9,d+9,d-9,d-9 is the result of multiplying all factors the greatest number of times they occur in either term.
(d+9)(d-9)
(d+9)(d-9)
Multiply each term by (d+9)(d-9) and simplify.
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Multiply each term in 16d+9-12(d+9)(d-9)=10d-9 by (d+9)(d-9) in order to remove all the denominators from the equation.
16d+9⋅((d+9)(d-9))-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Simplify 16d+9⋅((d+9)(d-9))-12(d+9)(d-9)⋅((d+9)(d-9)).
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Simplify each term.
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Cancel the common factor of d+9.
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Cancel the common factor.
16d+9⋅((d+9)(d-9))-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Rewrite the expression.
16⋅(d-9)-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
16⋅(d-9)-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Apply the distributive property.
16d+16⋅-9-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Multiply 16 by -9.
16d-144-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Cancel the common factor of (d+9)(d-9).
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Move the leading negative in -12(d+9)(d-9) into the numerator.
16d-144+-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Cancel the common factor.
16d-144+-12(d+9)(d-9)⋅((d+9)(d-9))=10d-9⋅((d+9)(d-9))
Rewrite the expression.
16d-144-12=10d-9⋅((d+9)(d-9))
16d-144-12=10d-9⋅((d+9)(d-9))
16d-144-12=10d-9⋅((d+9)(d-9))
Subtract 12 from -144.
16d-156=10d-9⋅((d+9)(d-9))
16d-156=10d-9⋅((d+9)(d-9))
Simplify 10d-9⋅((d+9)(d-9)).
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Cancel the common factor of d-9.
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Factor d-9 out of (d+9)(d-9).
16d-156=10d-9⋅((d-9)(d+9))
Cancel the common factor.
16d-156=10d-9⋅((d-9)(d+9))
Rewrite the expression.
16d-156=10⋅(d+9)
16d-156=10⋅(d+9)
Apply the distributive property.
16d-156=10d+10⋅9
Multiply 10 by 9.
16d-156=10d+90
16d-156=10d+90
16d-156=10d+90
Solve the equation.
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Move all terms containing d to the left side of the equation.
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Subtract 10d from both sides of the equation.
16d-156-10d=90
Subtract 10d from 16d.
6d-156=90
6d-156=90
Move all terms not containing d to the right side of the equation.
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Add 156 to both sides of the equation.
6d=90+156
Add 90 and 156.
6d=246
6d=246
Divide each term by 6 and simplify.
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Divide each term in 6d=246 by 6.
6d6=2466
Cancel the common factor of 6.
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Cancel the common factor.
6d6=2466
Divide d by 1.
d=2466
d=2466
Divide 246 by 6.
d=41
d=41
d=41
Solve for d 16/(d+9)-12/(d^2-81)=10/(d-9)

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