How to find the solution to a rational equation with LCD - SAT Math
Card 0 of 7
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In the equation below, 
, 
, and 
are non-zero numbers. What is the value of 
in terms of 
and 
?
In the equation below,
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Solve for x:
Solve for x:
The first step is to cancel out the denominator by multiplying both sides by 7:
Subtract 3 from both sides to get 
by itself:
The first step is to cancel out the denominator by multiplying both sides by 7:
Subtract 3 from both sides to get
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Solve for 
and 
using elimination:
Solve for
When using elimination, you need two factors to cancel out when the two equations are added together. We can get the 
in the first equation to cancel out with the 
in the second equation by multiplying everything in the second equation by 
:
Now our two equations look like this:
The 
can cancel with the 
, giving us:
These equations, when summed, give us:
Once we know the value for 
, we can just plug it into one of our original equations to solve for the value of 
:
When using elimination, you need two factors to cancel out when the two equations are added together. We can get the
Now our two equations look like this:
The
These equations, when summed, give us:
Once we know the value for
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Give the solution set of the rational equation 
Give the solution set of the rational equation
Multiply both sides of the equation by the denominator 
:
Rewrite both expression using the binomial square pattern:
This can be rewritten as a linear equation by subtracting 
from both sides:
Solve as a linear equation:
Multiply both sides of the equation by the denominator
Rewrite both expression using the binomial square pattern:
This can be rewritten as a linear equation by subtracting
Solve as a linear equation:
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Solve:
Solve:
Multiply by 
on each side
Subtract 
on each side
Multiply by 
on each side
Multiply by
Subtract
Multiply by
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