Algebra: Chapter 10, Lesson 6, page 451.
Solving Rational Expressions
We are now solving rational equations, they have an equal sign. With rational expressions on both side, we can sometimes structure these as ratios or proportions. We can solve proportions by criss-crossing, if `a/b = c /d`, then `a*d = b*c`. We just plug in the numerators and denominators where appropriate and work it out.
Remember too, that a quadratic equation has 0, 1 or at most 2 roots or answers. Sometimes, one of the solutions can be considered extraneous or invalid. Usually, it results in the denominator of an expression being = 0. In Algebra I, we don’t know how to handle that but eventually in higher math, you will.
Here is a link to the purplemath site with some more great information about rational equations.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 9, Lesson 3, page 411.
Equations and Absolute Value
To solve an equation of the form `| A | = b`, solve the disjunction `A = b` OR `A = −b`. You will have 2 equations to solve with the right side of the second equation having the opposite sign of the first equation’s right side.
REMEMBER by definition, the solution of `| A | ≠ a` NEGATIVE NUMBER! So … the solution to these type of problems is the NULL SET! or the symbol `∅` !
Two of tonight’s homework problems solved by MrE are here! Just click it!