Solution:
Denominator (both sides of the equation are multiplied at the same time)
common ground
, the fractional equation is transformed into
integral equation
)
; (2) According to the steps of solving the whole equation (
Interchange of terms
Combine similar terms
The coefficient is 1.
) Seek the unknown value.
; (3) Finding the root (after finding the value of the unknown quantity, the root must be found, because in the process of transforming the fractional equation into the whole equation, the unknown quantity is expanded.
Value range
, may produce
Zenggen
).
When finding the root, substitute the root of the whole equation into the simplest common denominator. If the simplest common denominator is equal to 0, this root is an added root. Otherwise, this root is the root of the original fractional equation. If the root of the solution is
Zenggen
The original equation has no solution.
If the score itself is about points, it should also be tested.
When solving an application problem with a column fraction equation, it is necessary to check whether the solution satisfies the equation and whether the solution satisfies the meaning of the problem.
factoring
1
Methods of improving common factor
: Generally speaking, if
multinomial
Each item has a common factor. You can put this common factor in parentheses and write the polynomial in the form of factor product. such
Decomposition factor
This method is called common factor method.
am+bm+cm=m(a+b+c)
use
Formula method
①
formula for the difference of square
:.
a^2-b^2=(a+b)(a-b)
②
Perfect square trinomial
a^2 2ab+b^2=(a b)^2
③
Cubic sum formula
:a^3+b^3=
(a+b)(a^2-ab+b^2).
Difference of cube
:a^3-b^3=
(a-b)(a^2+ab+b^2).
④
Complete cubic formula
a^3 3a^2b+3ab^2 b^3=(a b)^3
⑤a^n-b^n=(a-b)[a^(n- 1)+a^(n-2)b+……+b^(n-2)a+b^(n- 1)]
A m+b m = (a+b) [a (m-1)-a (m-2) b+...-b (m-2) a+b (m-1)] (m is an odd number).
three
Group multiplication
A method of grouping a polynomial and then factorizing it.
4. Methods of splitting and supplementing projects
Decomposition and supplement method: one term of polynomial is decomposed or filled with two terms (or several terms) which are opposite to each other, so that the original formula is applicable to common factor method, formula method or group decomposition method; It should be noted that the deformation must be carried out under the principle of equality with the original polynomial.
Cross multiplication
①x^2+(p
Factorization of q) x+pq formula
The characteristics of this kind of quadratic trinomial formula are: the coefficient of quadratic term is1;
constant term
Is the product of two numbers; The coefficient of a linear term is the sum of two factors of a constant term. So we can directly factorize some quadratic trinomial terms with a coefficient of 1:
x^2+(p
q)x+pq=(x+p)(x+q)
② Factorization of KX2+MX+N formula
If it can be decomposed into k = AC, n = BD, ad+BC = m.
So, when?
kx^2+mx+n=(ax
b)(cx
d)
a
\\ - /b
ac=k
bd=n
c
/ - \\d
ad+bc=m
take for example
Factorization x 2-x 2 = 0
Because x 2 = x times x
-2=-2 times 1
x
-2
x
1
Diagonal multiplication and addition =x-2x=-x
Horizontal writing (x-2)(x+ 1)
I hope you make progress.