1. The equation is of the form , where a, b, and c are all positive integers and . Using this equation as a model, create your own equation that has extraneous solutions. (a) Using trial and error with numbers for a, b, and c, create an equation of the form , where a, b, and c are all positive integers and such that 7 is a solution. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (b) Solve the equation you created in Part 2a. (c) If your solution in Part 2b did not have an extraneous solution, revise your equation so that 7 is one solution and there is an extraneous solution. If your solution in Part 2b did have an extraneous solution, create another equation with different values of a, b, and c that also has 7 as one solution and an extraneous solution.

--- equation

--- the equation is true for these values

--- the equation is extraneous for these values

Step-by-step explanation:

Given

Solving (a): Equation to solve for a, b and c, using trial by error where

We have:

Substitute 7 for x

--- This is the equation

Solving (b): Solve for a, b and c --- to make the equation true

Let a = 3 ----- Here, we choose a value for a

Square both sides

Let b = 5 --------- Here, we choose a value for b

Subtract 35 from both sides

So, is true for

Solving (b): Solve for a, b and c --- to make the equation false

Substitute

So, we have:

Square both sides

--- This is false

i.e.

n

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.