# Solve for a (a^2+51a)/(a^2+5a-14)-(a-7)/(a-2)=(a+1)/(a+7)

Factor each term.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
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 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The factor for is itself.
occurs time.
The factor for is itself.
occurs time.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Move to the left of .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Combine the opposite terms in .
Subtract from .
Simplify .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Multiply by .
Solve the equation.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Move all terms to the left side of the equation and simplify.
Move to the left side of the equation by subtracting it from both sides.
Subtract from .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
The final answer is the combination of both solutions.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for a (a^2+51a)/(a^2+5a-14)-(a-7)/(a-2)=(a+1)/(a+7)

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