Reducing Fractions To Their Lowest Terms - Tiger Algebra

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Step 1 :

n Simplify — n

Equation at the end of step 1 :

(8n - 3x) ((————————— - 4x) - 1) - x (x - n)

Step 2 :

8n - 3x Simplify ——————— x - n

Equation at the end of step 2 :

(8n - 3x) ((————————— - 4x) - 1) - x x - n

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using (x-n) as the denominator :

4x 4x • (x - n) 4x = —— = ———————————— 1 (x - n)

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(8n-3x) - (4x • (x-n)) -4x2 + 4xn - 3x + 8n —————————————————————— = ———————————————————— 1 • (x-n) 1 • (x - n)

Equation at the end of step 3 :

(-4x2 + 4xn - 3x + 8n) (—————————————————————— - 1) - x 1 • (x - n)

Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 1 • (x-n) as the denominator :

1 1 • 1 • (x - n) 1 = — = ——————————————— 1 1 • (x - n)

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

(-4x2+4xn-3x+8n) - (1 • x-n) -4x2 + 4xn - 4x + 9n ———————————————————————————— = ———————————————————— 1 • (x-n) 1 • (x - n)

Equation at the end of step 4 :

(-4x2 + 4xn - 4x + 9n) —————————————————————— - x 1 • (x - n)

Step 5 :

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 1 • (x-n) as the denominator :

x x • 1 • (x - n) x = — = ——————————————— 1 1 • (x - n)

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

(-4x2+4xn-4x+9n) - (x • (x-n)) -5x2 + 5xn - 4x + 9n —————————————————————————————— = ———————————————————— 1 • (x-n) 1 • (x - n)

Final result :

-5x2 + 5xn - 4x + 9n ———————————————————— x - n

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