The statement, "Clearing fractions is valid procedure only when solving equations not when adding, subtracting, multiplying or dividing rational expressions." is true or false

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The statement, &quot;Clearing fractions is valid procedure only when solving equations not when adding, subtracting, multiplying or dividing rational expressions.&quot; is true or false

servidopolisxv · Accepted Answer

Clearing fractions in case of equations is valid because in case of equations equal denominator on both sides can be cancelled without affecting the solution.  But in case of expressions, clear fractions affect the actual solution or may lead to wrong solution.  For example,  Consider an equation x2+1=23.  To solve the equation, clear the fraction so that it becomes easy to obtain the value of variable x as,  2(x2+1)=2(23)  x+2=43  x=43−2  x=−23  When the above equation is multipled by 2 to clear the fraction, the value of equation is not affected.  Now consider an expression x4.  To clear the fraction, multiply the above expression by 4 as,  x4⋅4=x  So, the fraction got cleared but the value of the expression is changed as x4 and x are two different expressions.  Hence, the statement, &quot;Clearing fractions is a valid procedure only when solving equations not when adding, subtracting, multiplying or dividing rational expressions.&quot; is true.

Durst37 · Accepted Answer

Step 1  Given: x2+1=23  Multiply both sides of the equation by 6, the least common multiple of 2, 3.  3x+6=4  Subtract 6 from both sides.  3x=4−6  Subtract 6 from 4 to get -2.  3x=−2  Divide both sides by 3.  x=−23  Fraction −23 can be rewritten aas −23 by extracting the negative sign.  x=−23

The statement, "Clearing fractions is valid procedure only when solving

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