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

Math
8t-7=3-4t-7
Find the LCD of the terms in the equation.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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).
Tap for more steps…
Simplify each term.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
Rewrite the equation as 3t-25=8.
3t-25=8
Move all terms not containing t to the right side of the equation.
Tap for more steps…
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.
Tap for more steps…
Divide each term in 3t=33 by 3.
3t3=333
Cancel the common factor of 3.
Tap for more steps…
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)

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top