Solve for y -1/(y+4)=-1(y+4)

Math
-1y+4=-1(y+4)
Factor each term.
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Apply the distributive property.
-1y+4=-1y-1⋅4
Rewrite -1y as -y.
-1y+4=-y-1⋅4
Multiply -1 by 4.
-1y+4=-y-4
-1y+4=-y-4
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.
y+4,1,1
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 y+4 is y+4 itself.
(y+4)=y+4
(y+4) occurs 1 time.
The LCM of y+4 is the result of multiplying all factors the greatest number of times they occur in either term.
y+4
y+4
Multiply each term by y+4 and simplify.
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Multiply each term in -1y+4=-y-4 by y+4 in order to remove all the denominators from the equation.
-1y+4⋅(y+4)=-y⋅(y+4)-4⋅(y+4)
Cancel the common factor of y+4.
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Move the leading negative in -1y+4 into the numerator.
-1y+4⋅(y+4)=-y⋅(y+4)-4⋅(y+4)
Cancel the common factor.
-1y+4⋅(y+4)=-y⋅(y+4)-4⋅(y+4)
Rewrite the expression.
-1=-y⋅(y+4)-4⋅(y+4)
-1=-y⋅(y+4)-4⋅(y+4)
Simplify -y⋅(y+4)-4⋅(y+4).
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Simplify each term.
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Apply the distributive property.
-1=-y⋅y-y⋅4-4⋅(y+4)
Multiply y by y by adding the exponents.
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Move y.
-1=-(y⋅y)-y⋅4-4⋅(y+4)
Multiply y by y.
-1=-y2-y⋅4-4⋅(y+4)
-1=-y2-y⋅4-4⋅(y+4)
Multiply 4 by -1.
-1=-y2-4y-4⋅(y+4)
Apply the distributive property.
-1=-y2-4y-4y-4⋅4
Multiply -4 by 4.
-1=-y2-4y-4y-16
-1=-y2-4y-4y-16
Subtract 4y from -4y.
-1=-y2-8y-16
-1=-y2-8y-16
-1=-y2-8y-16
Solve the equation.
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Rewrite the equation as -y2-8y-16=-1.
-y2-8y-16=-1
Move 1 to the left side of the equation by adding it to both sides.
-y2-8y-16+1=0
Add -16 and 1.
-y2-8y-15=0
Factor the left side of the equation.
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Factor -1 out of -y2-8y-15.
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Factor -1 out of -y2.
-(y2)-8y-15=0
Factor -1 out of -8y.
-(y2)-(8y)-15=0
Rewrite -15 as -1(15).
-(y2)-(8y)-1⋅15=0
Factor -1 out of -(y2)-(8y).
-(y2+8y)-1⋅15=0
Factor -1 out of -(y2+8y)-1(15).
-(y2+8y+15)=0
-(y2+8y+15)=0
Factor.
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Factor y2+8y+15 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 15 and whose sum is 8.
3,5
Write the factored form using these integers.
-((y+3)(y+5))=0
-((y+3)(y+5))=0
Remove unnecessary parentheses.
-(y+3)(y+5)=0
-(y+3)(y+5)=0
-(y+3)(y+5)=0
Multiply each term in -(y+3)(y+5)=0 by -1
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Multiply each term in -(y+3)(y+5)=0 by -1.
(-(y+3)(y+5))⋅-1=0⋅-1
Simplify (-(y+3)(y+5))⋅-1.
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Simplify by multiplying through.
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Apply the distributive property.
(-y-1⋅3)(y+5)⋅-1=0⋅-1
Multiply -1 by 3.
(-y-3)(y+5)⋅-1=0⋅-1
(-y-3)(y+5)⋅-1=0⋅-1
Expand (-y-3)(y+5) using the FOIL Method.
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Apply the distributive property.
(-y(y+5)-3(y+5))⋅-1=0⋅-1
Apply the distributive property.
(-y⋅y-y⋅5-3(y+5))⋅-1=0⋅-1
Apply the distributive property.
(-y⋅y-y⋅5-3y-3⋅5)⋅-1=0⋅-1
(-y⋅y-y⋅5-3y-3⋅5)⋅-1=0⋅-1
Simplify and combine like terms.
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Simplify each term.
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Multiply y by y by adding the exponents.
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Move y.
(-(y⋅y)-y⋅5-3y-3⋅5)⋅-1=0⋅-1
Multiply y by y.
(-y2-y⋅5-3y-3⋅5)⋅-1=0⋅-1
(-y2-y⋅5-3y-3⋅5)⋅-1=0⋅-1
Multiply 5 by -1.
(-y2-5y-3y-3⋅5)⋅-1=0⋅-1
Multiply -3 by 5.
(-y2-5y-3y-15)⋅-1=0⋅-1
(-y2-5y-3y-15)⋅-1=0⋅-1
Subtract 3y from -5y.
(-y2-8y-15)⋅-1=0⋅-1
(-y2-8y-15)⋅-1=0⋅-1
Apply the distributive property.
-y2⋅-1-8y⋅-1-15⋅-1=0⋅-1
Simplify.
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Multiply -y2⋅-1.
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Multiply -1 by -1.
1y2-8y⋅-1-15⋅-1=0⋅-1
Multiply y2 by 1.
y2-8y⋅-1-15⋅-1=0⋅-1
y2-8y⋅-1-15⋅-1=0⋅-1
Multiply -1 by -8.
y2+8y-15⋅-1=0⋅-1
Multiply -15 by -1.
y2+8y+15=0⋅-1
y2+8y+15=0⋅-1
y2+8y+15=0⋅-1
Multiply 0 by -1.
y2+8y+15=0
y2+8y+15=0
Factor y2+8y+15 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 15 and whose sum is 8.
3,5
Write the factored form using these integers.
(y+3)(y+5)=0
(y+3)(y+5)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y+3=0
y+5=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
y+3=0
Subtract 3 from both sides of the equation.
y=-3
y=-3
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
y+5=0
Subtract 5 from both sides of the equation.
y=-5
y=-5
The final solution is all the values that make (y+3)(y+5)=0 true.
y=-3,-5
y=-3,-5
Solve for y -1/(y+4)=-1(y+4)

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