# Solve for t 8/(t-7)=3-4/(t-7)

8t-7=3-4t-7
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.
t-7,1,t-7
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 t-7 is t-7 itself.
(t-7)=t-7
(t-7) occurs 1 time.
The LCM of t-7,t-7 is the result of multiplying all factors the greatest number of times they occur in either term.
t-7
t-7
Multiply each term by t-7 and simplify.
Multiply each term in 8t-7=3-4t-7 by t-7 in order to remove all the denominators from the equation.
8t-7⋅(t-7)=3⋅(t-7)-4t-7⋅(t-7)
Cancel the common factor of t-7.
Cancel the common factor.
8t-7⋅(t-7)=3⋅(t-7)-4t-7⋅(t-7)
Rewrite the expression.
8=3⋅(t-7)-4t-7⋅(t-7)
8=3⋅(t-7)-4t-7⋅(t-7)
Simplify 3⋅(t-7)-4t-7⋅(t-7).
Simplify each term.
Apply the distributive property.
8=3t+3⋅-7-4t-7⋅(t-7)
Multiply 3 by -7.
8=3t-21-4t-7⋅(t-7)
Cancel the common factor of t-7.
Move the leading negative in -4t-7 into the numerator.
8=3t-21+-4t-7⋅(t-7)
Cancel the common factor.
8=3t-21+-4t-7⋅(t-7)
Rewrite the expression.
8=3t-21-4
8=3t-21-4
8=3t-21-4
Subtract 4 from -21.
8=3t-25
8=3t-25
8=3t-25
Solve the equation.
Rewrite the equation as 3t-25=8.
3t-25=8
Move all terms not containing t to the right side of the equation.
Add 25 to both sides of the equation.
3t=8+25
Add 8 and 25.
3t=33
3t=33
Divide each term by 3 and simplify.
Divide each term in 3t=33 by 3.
3t3=333
Cancel the common factor of 3.
Cancel the common factor.
3t3=333
Divide t by 1.
t=333
t=333
Divide 33 by 3.
t=11
t=11
t=11
Solve for t 8/(t-7)=3-4/(t-7)

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