Solving fractional equations, how to solve fractional equations

The first group: -=1, i.e. 2 x+y=1, x+y=2 y+z=3, z+x=4

All add up to 2x+2y+2z=9, x+y+z= to get x=,y=,z=

Since I haven't learned fractional equations, it's still difficult for me to solve the second set of difficulties.

Equation 1: Equation 1 - Equation 3 + Equation 2: 2 (y+z)=10 12-9 12+7 12=8 12=2 3 yields: y+z=3

Substituting the formula, we get: x+y=2;z+x=4

x+y-z-x+y+z=2-4+3=1 y=1 2 is substituted into the formula to get x=1(1 2) z=2(1 2).

The second equation of the second system of equations is wrong. It should be (xz+2x) (x+z+2)=3

First, take the reciprocal of the three equations to get 1 x+1 (y+1)=1 2(1), 1 x+1 (z+2)=1 3(2), 1 (y+1)+1 (z+2)=1 4(3).

Add the three formulas to yield: 1 x+1 (y+1)+1 (z+2)=13 24.

Subtract (1), (2), and (3) respectively to obtain: x=24 7, y=19 5, z=22.

1.When solving the fractional equation, often multiply the two sides of each fractional equation in the equation system by the appropriate integer (the lowest common multiple of the denominator), deform it into an integer equation, and then solve this integral equation, because the two sides of the equation are multiplied by the appropriate integral non-identical solution, there is the possibility of increasing the root, therefore, the solution of the obtained integral equation must be substituted into the multiplied integer or substituted into the original equation system for testing.

2.The basic idea of solving fractional equations is to "turn fractional equations into integral equations", and similarly, the basic idea of solving fractional equations is to "transform fractional equations into integral equations", that is, to convert every fractional equation in the equation into an integral equation.

3.To solve a system of fractional equations, you can turn it into an integral system of equations and then solve it, and sometimes you can use different methods to solve the problem according to the characteristics of the system of equations.

4.When solving fractional equations, because in the process of deformation, an integer containing unknown numbers is used to multiply both sides of the equation and reduce the denominator, so root addition may occur, so the root verification step is also essential for solving fractional equations.

Multiply by 3 to get the formula 6 x+9 y=24 Multiply by 2 to get the formula 6 x=4 y=14 - get 5 y=10, get y=

Substituting the solution yields x=1

The first equation is *20, and the two equations are subtracted to get y=120 and x=30

Multiply one by four, and subtract one by two, to get 5 y = 1 3

Derives y=15

Let 1 x=a, 1 y=b, i.e., a+b=1 6 multiply both sides by 4 to get 4a+4b=2 3 (1).

4a+9b=1 (2)

2)-(1) gives 5b=1 3 gets b=1 15 and brings it into the original formula to get a=1 6-1 15=1 10

Therefore x=10, y=15

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Teach me the steps. Okay, wait a minute.

Solution: 6 x + 6 y = 4 x + 9 y

Then 2 x = 3 y, then 2y = 3x, i.e. y = 3, 2) x

Bring in any of the equations to get y=15 x=10

Let a=1 x, b=1 y, i.e., be reduced to a system of binary equations:

a+b=1/6-->4a+4b=2/3

4a+9b=1

5b=1 3-->b=1 15---a=1 6-1 15=1 10 Therefore. x=1/a=10,y=1/b=15

The first pass points become.

6y+6x)/xy=1

4y+9x)/xy=1

6y+6x=4y+9x

y=3 2x is brought into the original formula to solve x=10, y=15

3/(3x＋2y)＋1/(4x－y)=13/12 ①

4/(3x＋2y)＋6/(4x－y)=3。Note the denominator of the equation, which can be solved using the commutation method.

Let m=1 (3x 2y) and n=1 (4x y). Then the original equation can be reduced to:

3m＋n=13/12

4m 6n=3, find: m=1 4, n=1 3.

i.e.: 3x 2y=4

4x－y=3

So you can solve it, right? x=11/10，y=7/11。

No, therefore, a one-dimensional equation cannot have fractions.

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Observing the equation, the simplest common denominator is, multiplying both sides of the equation and solving it into an integral equation;

Since the coefficient of the unknown is timely, the substitution method can be used to solve the problem.

The solution: , after testing, is the root of the original equation; , gotta :

Solution: .Substituting the solution is obtained, so the solution of the equation is.

Solving fractional equations is mainly to convert fractional equations into integral equations to solve, and test them after solving.

When the coefficient of the unknown is is, the substitution method can be used to solve it. When the coefficients of the unknowns are opposite to each other, the addition, subtraction, and elimination method can be used to solve the problem. When the system of equations is more complex, it needs to be simplified first.

3x+2y=48 =>3x=48-2y

2y+6x=3xy =>2y+3x(2-y)=02y+(48-2y)(2-y)=0

y*y-25y+48=0

There is no solution to this question, confirm that the question is correct.