English
An algebraic fraction is an ordinary fraction wearing a disguise: the numbers have been swapped for letters, but every rule you learned for 3/4 still works for (x+1)/(x-2).
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English
Replace the 3 in 3/4 with (x+1) and the 4 with (x−2): you get (x+1)/(x−2). Every fraction rule from primary school still applies.
Simplifying
English
You may only cancel factors (things multiplied), never terms (things added). So (x²+x)/(x+1) becomes x(x+1)/(x+1) = x.
Multiply and divide
English
Factorise and cancel before multiplying to keep the algebra small. For division use KFC: Keep, Flip, Change.
Add and subtract
English
If the bottoms share no factor, the common denominator is their product. Take care with the minus sign when subtracting.
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Point 1
Point 2
Point 3
Point 4
Point 5
Point 6
Point 7
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Point 1
An algebraic fraction obeys exactly the same rules as a number fraction.
Point 2
Factorising is the key skill: it lets you cancel and simplify.
Point 3
Always state restrictions: values of x that make a denominator zero.
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सामान्य भूल
✕ You can cancel the x in (x²+x)/(x+1) straight away.
✓ x is a term on top, not a factor. Factorise to x(x+1) first, then cancel.
सामान्य भूल
✕ (x+2)/(x+3) cancels to 2/3.
✓ Nothing cancels: (x+2) and (x+3) are sums, not products. They share no common factor.
सामान्य भूल
✕ To divide, just divide tops and divide bottoms.
✓ Flip the second fraction and multiply (KFC).
सामान्य भूल
✕ When subtracting, only the first number of the top changes sign.
✓ The minus applies to the whole second numerator: subtract every term, e.g. −3(x−1) = −3x + 3.
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