[Music] in this video we will illustrate rational algebraic expressions we will also evaluate rational algebraic expressions and we will find every value of the variables that makes a rational expression undefined so first let us define what is a rational algebraic expressions so it is a rational expression in one variable is an expression that can be written in the form p over q where p and q are polynomials so again p and q should be polynomials now these are the examples i have here four over x minus two four x all over x squared plus nine x squared plus two x minus 35 all over three x plus four now remember that your q or jung denominator nathan should not be equal to zero dahil kapag remember q should not be equal to zero for your expression not to be undefined okay so undefined expression and let's have an example how to evaluate algebraic expression simply by replacing the variable with a value so o ito so let us have an example evil with the expression x squared minus 4 all over x minus 2 when x is equal to 0 and x is equal to 1. let's have the first one so if your x is equal to zero so we will just replace the variable with the value which is zero so we will have zero and then another zero since we have two x's here and then our zero squared is zero so we will have negative four and then negative two so we will simplify negative four divided by negative two that is positive two next if x is equal to one so therefore we will assign or substitute one to the variable so we will have one squared minus four all over one minus two so we will just follow the okay so let us simplify your 1 squared is 1 minus 4 your denominator will become 1 minus 2 so this is negative 3 and then 1 minus 2 that is negative 1 so as you can see our denominator is negative one so since this is not zero therefore this is an algebraic expression so negative three divided by negative one that is positive three so as you can see a manga denominator is nothing i condition zero so e big sub hen uh x squared minus four all over x minus two happy value non variable nothing is zero and one it will not make the expression define another example so i have here x squared minus two all over x minus four so we will have x is equal to one that substitute also x is equal to two so let us try to uh evil weight so x squared minus 2 all over x minus 4 so we will substitute 1 and then another one so 1 squared is 1 minus 2 all over 1 minus 4 so 1 minus 2 is negative 1 1 minus 4 is negative 3 let us simplify so negative 1 all over negative 3 that is positive 1 3 next so we will substitute here positive two so we will replace the variable with two so we will now have two squared is four minus two and then two minus four so four minus two is two two minus 4 is negative 1 let us simplify 2 divided by negative 2 that is negative 1. so hindi renault 0 and denominator not and therefore this is an algebraic expression next evaluate the expression a squared minus two b all over a minus b so pa no no man capacitance variables net n so a is equal to one b is equal to two and another a is equal to two b is equal to three so let's have a squared minus two b all over a minus b so we will have one one for a two four b so one squared is one two times two is four so at the end and then one and then minus two so let us simplify one minus four that is negative three one minus two that is negative one so we will have positive three so eta junkies variables next so a is equal to two b is equal to three so we will have our if a is 2 our b is 3 so let us simplify 2 squared that is 4. let us simplify 2 times 3 that is 6 and then two minus three okay so we will have four minus six that is negative two two minus three that is negative one so negative two divided by negative one that is positive [Music] variable so you must have two assigned values for the variables now not then that is not considered rational algebraic expressions okay substitute so denominator undefined expression net in so to make a rational expression x squared minus 2 all over x minus 4 undefined first we will equate the denominator to 0 so what is our denominator x minus four since equate to zero so equals zero okay you know equate next solve for the variable so ililipatna in say negative four that will become x is equal to zero plus four let us simplify so we have x is equal to four so e big sub hand the expression x squared minus two all over x minus four is undefined if x is replaced by four because the denominator would be zero so assigned values of variable zero and denominator undefined so let us try if your x is equal to four so four minus four that is zero so eto and values which may cause your expression undefined another example so i have here x squared minus 4 all over x minus 2 so again our first step equate the denominator to zero so that is x minus two equals zero solve for the variable so we will transpose a negative two so that is x is equal to zero plus two so that is x is equal to 2. so therefore the expression x squared minus 4 all over x minus 2 is undefined if x is replaced by 2 because the denominator would be zero so ethereum value non-variable nahindi pueden is substituting expression that will make your expression a rational expression undefined so let us try if this is 2 2 minus 2 that would become zero so hindi another so to make a rational expression x squared minus y all over x minus y undefined so this is another case if you are given two variables so equate the denominators to zero and the pattern value exit y para hindi shaman undefined okay so annoying so equate the denominator by zero so we will have x minus y equals zero solve for the variable so that is x is equal to zero plus y so making x is equals to y so e big sub b hand the expression x squared minus y all over x minus y is undefined if the variables or the value of the variables x and y are replaced by equal values that would mean undefined capacity i same values or equal values at synaptic expression nato hindisha rational expression let us try if this is 2 so this is also 2 so 2 minus 2 that is 0. if this is 4 and this is also 4 so 4 minus 4 that is 0. so hapag and value num x at waymo are equal values that would make your expression undefined now test yourself you may pause the video so you can answer on your own next thank you for watching this video i hope you learned something don't forget to like subscribe and hit the notification bell for updated ko for more video tutorials this is your guide in learning your math lessons your walmart channel