x+7x=-8

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

1,x,1

Since 1,x,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1 then find LCM for the variable part x1.

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 x1 is x itself.

x1=x

x occurs 1 time.

The LCM of x1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

x

x

Multiply each term in x+7x=-8 by x in order to remove all the denominators from the equation.

x⋅x+7x⋅x=-8⋅x

Simplify each term.

Multiply x by x.

x2+7x⋅x=-8⋅x

Cancel the common factor of x.

Cancel the common factor.

x2+7x⋅x=-8⋅x

Rewrite the expression.

x2+7=-8⋅x

x2+7=-8⋅x

x2+7=-8x

x2+7=-8x

Add 8x to both sides of the equation.

x2+7+8x=0

Factor x2+7+8x using the AC method.

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 7 and whose sum is 8.

1,7

Write the factored form using these integers.

(x+1)(x+7)=0

(x+1)(x+7)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x+1=0

x+7=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

x+1=0

Subtract 1 from both sides of the equation.

x=-1

x=-1

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

x+7=0

Subtract 7 from both sides of the equation.

x=-7

x=-7

The final solution is all the values that make (x+1)(x+7)=0 true.

x=-1,-7

x=-1,-7

Solve for x x+7/x=-8