Remove the denominator and brackets first. If it is necessary to shift terms and merge similar terms, the coefficient obtained is 1, which is substituted into the equation, and the equation group is transformed into a linear equation with one variable to get the answer. Some methods to calculate the quantitative relationship in simple practical problems in the form of binary linear equations and to learn to express another with algebraic expressions containing one unknown are all based on linear equations with one variable.

There are algebraic expressions on both sides, and there are two unknowns. An equation with the unknown degree of 1 is called a binary linear equation. The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.

I. One-dimensional equation

One-dimensional linear equation is the simplest equation, and its form is: ax+b=0, where a and b are known constants and x is unknown. The basic idea of solving a linear equation with one variable is to shift terms and merge similar terms. The specific solving steps are as follows:

1. Convert the equation into the standard form: ax =-b;

2. Solve the equation to get the value of x: x =-b/a, for example, for the equation 3x-4=0, we can convert it into 3x=4, and finally get x=4/3.

Second and quadratic equation

The unary quadratic equation is an equation in the form of ax2+bx+c-=0, where A, B and C are known constants and a#0. The common methods to solve equations are factorization, collocation method, root formula and so on.

1. Factorization method: When the quadratic equation can be factorized, the solution of the equation can be obtained by solving the factors of the equation. For example, the equation x2-5x+6=0 can be factorized into (x-2)(x-3)=0, and then x=2 or x=3 can be obtained.

2. Matching method: by choosing appropriate parameters, the quadratic equation of one variable is transformed into a completely flat way, and then the idea of solving the equation is solved. For example, the equation x2-6x+8=0 can be formulated as (x-3)2- 1=0, and then (x-3)2= 1 can be obtained, and x=2 or x=4 can be solved.

3. Root formula method: the solution of quadratic equation in one variable can be obtained by root formula. The formula for finding the root is x = (-b√ (b-4ac))/(2a). For example, for the equation x2-2x-3=0, x=3 or x=- 1 can be calculated by the root formula.

Third, one-dimensional higher-order equation

One-dimensional high-order equation refers to one-dimensional equation with degree greater than 2, such as cubic equation and quartic equation. The methods of solving univariate higher order equations are complicated, including rational root theorem, comprehensive division, mirror image method and so on.

1. rational root theorem: the rational root theorem points out that if the unary higher-order equation axn+a _ (n-1) x (n-1)+ax+ao = 0 has a rational root p/q(p, q is coprime), then p is a constant term. Q is the factor of the first coefficient A. By finding the possible rational root, and then verifying it by comprehensive division, the solution of the equation is finally obtained.

2. Comprehensive division: Comprehensive division is a method to obtain unknown values through the existing form of division. Through comprehensive division, we can find the roots of the equation one by one, and finally simplify the equation into a one-dimensional linear equation, and then solve it.

3. Mirror image method: For the univariate high-order equation, we can get the solution of the equation by drawing the mirror image of the equation. By observing the intersection and trend of images, the number and distribution of solutions of the equation can be obtained.