Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We need to solve the inequality $\frac{4}{|x-1|+1} - \frac{5}{|x-1|-2} \geq 0$.

InequalitiesAbsolute ValueAlgebraic Manipulation

We need to solve the following inequality: $\frac{2}{|x-3|-1} + \frac{3}{|x-3|+2} \leq 0$

InequalitiesAbsolute ValueIntervalsSolving Inequalities

We need to solve the inequality $\frac{|x-1|}{x} < 0$.

InequalitiesAbsolute ValueInterval Notation

The problem is to solve the equation $\frac{2mx(m+1)+3x}{m^3-27} - \frac{x}{m-3} + \frac{x+1}{m^2+3m...

EquationsAlgebraic ManipulationFactoringRational Expressions

We are asked to solve the equation $\frac{2mx(m+1)+3x}{m^3-27} - \frac{x}{m-3} + \frac{x+1}{m^2+3m+9...

Algebraic EquationsRational ExpressionsEquation SolvingFactorizationDifference of CubesVariable Isolation

We are asked to verify the given equation: $\frac{x+a+b}{x-a-b} + \frac{x-a-b}{x+a+b} = \frac{2(x^2 ...

Algebraic ManipulationEquationsSimplificationIdentities

The problem is to verify the following equation: $\frac{x+a+b}{x-a-b} + \frac{x-a-b}{x+a+b} = \frac{...

Equation VerificationAlgebraic ManipulationSimplificationRational Expressions

We are given the equation: $\frac{1}{(x-a-b)(x+a+b)} + \frac{1}{x^2 + a^2 + b^2 - 2ax - 2bx + 2ab} =...

Equation VerificationAlgebraic ManipulationRational Expressions

We are given the equation: $\frac{1}{(x-a-b)(x+a+b)} + \frac{1}{x^2+a^2+b^2-2ax-2bx+2ab} = \frac{2}{...

Equation VerificationAlgebraic ManipulationFractionsError Analysis

We are given the equation: $\frac{1}{(x-a-b)(x+a+b)} + \frac{1}{x^2 + a^2 + b^2 - 2ax - 2bx + 2ab} =...

Algebraic EquationsEquation VerificationSimplificationExpansion

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